UNIVERSITY OF BOLTON ENGINEERING ,SPORTS · PDF file... During the isothermal heat rejection process of a Carnot ... working fluid experiences an entropy change of ... that operates

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UNIVERSITY OF BOLTON

ENGINEERING ,SPORTS AND SCIENCES ACADEMIC GROUP

BENG (HONS) IN MECHANICAL ENGINEERING

SEMESTER 1 EXAMINATION 2014/2015

ADVANCED THERMOFLUIDS & CONTROL

SYSTEMS

MODULE NO: AME6005

Date: 21 January 2015 Time: 10.00 – 12.00

INSTRUCTIONS TO CANDIDATES: There are SIX questions.

Answer ANY FOUR questions.

All questions carry equal marks.

Marks for parts of questions are

shown in brackets.

This examination paper carries a total

of 100 marks.

All working must be shown. A

numerical solution of a question

obtained by programming an

electronic calculator will not be

accepted.

CANDIDATES REQUIRE : Thermodynamic properties of fluids

provided

Formula Sheet provided

Take density of water as 1000 kg/m3

Page 3 of 20

Engineering, Sports &Sciences Academic Group BEng (Hons) Mechanical Engineering Semester 1 Examination 2014/2015 Advanced Thermofluids & Control Systems Module No: AME6005

Q1 (a) A thin rectangular plate having a width (w) and a height (h) is located

so that it is normal to a moving stream of fluid. Assume the draft D that

the fluid exerts on the plate is a function of w and h, the fluid viscosity,

density and the velocity of fluid approaching the plate. Determine a

suitable set of pi terms to study this problem experimentally.

(15 marks)

(b) Water at 30ºC is flowing through a pipe 2cm in diameter with a velocity

of 30 cm/s. is the flow laminar or turbulent? Also classify the flow if

the fluid is glycerine.

Take kinematic viscosity for water = 0.804 10-6 m2/s Density of water at 30ºC = 995.7 kg/m3

Viscosity of glycerine = 8620 10-6 ns/m2 Specific gravity for glycerine = 1.26 (10 marks)

Total 25 marks

Q2 (a) One kg of water at 273K is brought into contact with a heat reservoir at

373K. When the water has reached 373K find the entropy change.

Take Cv = 4.217 KJ/KgK. (8 marks)

(b) 1kg of steam at 15 bar, dryness fraction 0.8 is heated reversibly at

constant pressure to a temperature of 300oC. Draw the T-S diagram,

and calculate the heat supplied and the change of entropy.

(17 marks)

Total 25 marks

Please turn the page

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Q3 (a) During the isothermal heat rejection process of a Carnot cycle, the

working fluid experiences an entropy change of -0.6KJ/K. If the

temperature of the energy sink is 30oC, determine:

(i) The amount of heat transfer to the sink (5 marks)

(ii) the entropy change of the sink and (5 marks)

(iii) the total entropy change for this process (5 marks)

(b) Consider a 200 MW steam power plant that operates on a simple ideal

Rankin Cycle. Steam enters the turbine at 10MPa and 500oC and is

cooled in a condenser at a pressure of 10KPa. Show the cycle on T-s

diagram with respect to saturation lines and determine:-

(i) The quality of the steam at the turbine exit

(ii) The thermal efficiency of the cycle

(10 marks)

Total 25 marks

Please turn the page

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Q4. Figure Q4 shows a CNC control system, which requires high accuracy for

position and velocity response. If the CNC system has a transfer function of:

)32)(8(

1)(

ssssGp

and a controller is used in the system.

Figure Q4 A CNC Control System

(a) If a PI controller is used (Kp = K, Kd, = 0) determine the integral gain Ki

to control the system’s steady state error be less than 0.2. The system

subjects a unit parabolic function (θi = 3

1

s). (7 marks)

(b) Design a PD controller (Ki = 0) that will meet the system design

specifications ts = 4s and percentage overshoot = 10%. Use a second-

order approximation to determine the proportional gain Kp and the

derivative gain Kd. The system subjects a unit step input.

(12 marks)

Question 4 continued overleaf

i(s) CNC system

Gp(s)

Controller

Gc(s)

o(s)

-

Page 6 of 20


Question 4 continued

(c) For a PID controller, briefly explain:

For which purpose a P is needed

For which purpose an I is needed

For which purpose a D is needed (6 marks)

(Total 25 marks)

Q5 (a) Give one example of analogue system and one example of digital

system and explain, helped by sketches, how the signal is carried both

in the analogue system and in the digital system. (6 marks)

(b) If a controller has a 10 bit Analogue to Digital Converter with the signal range between -24 Volt to +24 Volt:

(i) What is the resolution of the AD converter? (2 marks)

(ii) What integer number represented a value of 10 Volts? (2 marks)

(iii) What voltage does the integer 300 represent? (2 marks)

(iv) What voltage does 1100101011 represent? (2 marks)

(c) A controller (as shown in Figure Q5(c)) consists of a Digital to Analogue

Converter with zero order element in series with the processing centre

which has a transfer function

)10(

10)(

sssG

(i) Find the sampled-data transfer function G(z) for the digital control system. The sampling time, T, is 0.05 seconds. (7 marks)

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(ii) Find the steady-state error for the feedback control system as

shown in Figure Q5(c), if the input to the system is a unit step input. (4 marks)

Figure Q5(c) Digital Feedback Control System

(Total 25 marks)

Q6 (a) Describe the major features for the following control methods:

Laplace Transforms (in s domain) methods

Frequency Responses (in ω domain) methods

State-Space (or time-domain) methods (9 marks)

(b) Figure Q6(b) shows a simplified mechanical system.

(i) Derive the differential equations describing the behaviour of the system. (6 marks)

(ii) Select the state variables and transfer the differential equations obtained from (i) above to the relevant first-order differential equations. (4 marks)

(iii) Determine the state space equations and system matrices A, B, C and D, where A, B, C, and D have their usual meaning and

(6 marks)

8.05.0

8)(

2

zz

zzG

U(z) X(z)

Page 8 of 20




Figure Q6(b) A Simplified Mechanical System

(Total 25 marks)

END OF QUESTIONS

X1

F

M2

M1

K1

X2

K2

C1 C2

Page 9 of 20


FORMULA SHEETS

W = P (v2 – v1)

V

V PV = W

1

2ln

Q = Cd A √2gh

12 21

g

ghgCV m

.ΔMΔt

ΔMF

F = ρ QV

Re = V L ρ/

dQ = du + dw

du = cu dT

dw = pdv

pv = mRT

h = hf + xhfg

s = sf + xsfg

v = x Vg

hm w - Q...

1 -n

V P - V P =W 2211

Page 10 of 20


3

2

2

R

RL

LF

n

T

dQds

1

2n12 L

T

TCSS pL

f

fg

pLgT

hTCS

273L n

f

pu

f

gf

pLT

TC

T

hfTCS nn L

273L

1

2n

1

2np12

P

PMRL

T

TL MCSS

sCDFD

2u 2

1

suFL

2

LC 2

1

)( gZPds

dS p

L

pDQ

128

4

gD

L

Rh f

2

v64 2

Page 11 of 20


Re

16f

g2d

fLv4h

2

f

g

Khm

2

v2

g

VVkhm

2

2

21

H

L

T

T1

T

QSSSgen )12

geno STSSTUUW 02121 )(

)( 12 VVPWW ou

)()()( 21021021 VVPSSTUUWrev

)()()( 00 oVVPoSSTUU

genToSI

Page 12 of 20


1000

gQHp

RRt60

NT

R

RL

uL2F

t

V

rV

4

2

4

1

2

1

2n

Page 13 of 20


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G(s) = )()(1

)(

sHsGo

sGo

(for a negative feedback)

G(s) = )()(1

)(

sHsGo

sGo

(for a positive feedback)

Steady-State Errors

)]())(1([lim0

ssGse iOs

ss

(for an open-loop system)

)]()(1

1[lim

0s

sGse i

os

ss

(for the closed-loop system with a unity feedback)

)](

]1)()[(1

)(1

1[lim

1

10

s

sHsG

sGse i

sss

(if the feedback H(s) ≠ 1)

])1)((1

)([lim

12

2

0d

sss

sGG

sGse

(if the system subjects to a disturbance input)

Laplace Transforms A unit impulse function 1

A unit step function s

1

A unit ramp function 2

1

s

First order Systems

)1( / t

ssO eG (for a unit step input)

)1( / t

ssO eAG (for a step input with size A)

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Performance measures for second-order systems

dtr = 1/2

dtp =

P.O. = exp %100))1(

(2

ts = n

4

d = n(1-2)

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UNIVERSITY OF BOLTON ENGINEERING ,SPORTS · PDF file... During the isothermal heat rejection process of a Carnot ... working fluid experiences an entropy change of ... that operates