UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING · PDF filePage 3 of 18 School of Engineering BEng (Hons) Mechanical Engineering Semester 1 Examination 2017/2018 Advanced Thermofluids &

ENG001

UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING

BENG (HONS) IN MECHANICAL ENGINEERING

SEMESTER 1EXAMINATION 2017/2018

ADVANCED THERMOFLUIDS & CONTROL

SYSTEMS

MODULE NO: AME6005

Date: 18 January 2018 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 18

School of Engineering BEng (Hons) Mechanical Engineering Semester 1 Examination 2017/2018 Advanced Thermofluids & Control Systems Module No: AME6005

Q1 a) Steam at 110 bar has a specific volume of 0.0196 m3/kg, using the property tables find the:

i) Temperature ii) Enthalpy iii) The internal energy

(10 marks)

b) 1 kg of steam at 7 bar and entropy of 6.5kJ/kg K is heated reversibly at constant pressure until the temperature is 250 oc. calculate the heat supplied and show on a –T-S diagram the area which represents the heat flow.

(15 marks)

Total 25 marks

Q2 a) explain with the aid of diagram the simple Rankine cycle. (12 marks)

b) A collar bearing has external and internal diameters 200 mm and 160 mm respectively. The collar at the bearing surfaces are separated by an oil film 2 mm thick. Find the power lost in overcoming friction when the shaft is rotating at 250 rpm. Take the dynamic viscosity as 0.9 N s/m2.

(13 marks)

Total 25 marks

Q3 a) Water flow in a circular conduit where there are different diameters.

Diameter D1 = 2m changes into D2 = 3m. The velocity in the entrance profile was measured as 3 m/s. Determine:

i) The discharge at the outlet ii) The mean velocity at the outlet iii) The type of flow in both conduit profiles

Take the kinematic viscosity as 124 ˣ 10 -6 m 2 /s

(10 marks)

Question 3 continues overleaf

Please turn the page

Page 4 of 18


Question 3 continued

b) A prototype valve which will control the flow in a pipe system converting paraffin is to be studied in a model. The pressure drop ∆P is expected to depend upon the gate opening h, the overall depth d, the velocity v, the density ρ and viscosity μ. Perform dimensional analysis to obtain the relevant non dimensional groups.

(15 marks) Total 25 marks

Q4 A PID controller designed to control a position of a moving mechatronic

system is shown in Figure Q4. The transfer function of the plant is

)610(

1)(

sssGp

Gc(s) Gp(s) +

-

Input(s) Output(s)

Figure Q4

The design criteria for this system are:

Settling time < 3.5 sec Overshoot < 15% Steady state error < 5% (for a unit parabolic input = 1/s3)

a) Design a PID controller to determine the parameters Kp, Ki, and Kd and

clearly identify the design procedure. (15 marks)

Question4 continues overleaf


Page 5 of 18



b) If a velocity feedback is introduced into Figure Q4 and suppose

Gc(s) = 5, i) draw a block diagram with the velocity feedback and explain

the effects on a control system of including the velocity feedback.

(4 marks) ii) determine the velocity gain Kv for the damping ratio to be

increased as 0.8. (6 marks)

Total 25 marks

Q5 Figure Q5 shows a manufacturing system which includes a machining centre, a sensor system, and a controller.

Figure Q5 A manufacturing system

The machining centre (an analogue system) is controlled by the controller (a computer numerical control). The sensor system (an analogue system) detects the machining conditions and feedback the detected information to the controller. a) Draw a closed-loop control system, with the help of a block diagram, for

the manufacturing system shown in Figure Q5. Clearly identify all the

Controller

Sensor System

Gs(s)

Machining Centre

Gp(s)

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components and explain how the whole closed-loop control system works.

(6 marks)

Question 5 continues overleaf



b) If the manufacturing control system’s resolution required is 4 mV, and the range of sensor system varies between -8 Volt to +8 Volt,

i) Design an Analogue to Digital Converter with suitable bits for the

manufacturing controller. (4 marks)

ii) What integer number represented a value of +4 Volts?

(2 marks)

iii) What voltage does the integer 800 represent? (2 marks)

c) If the manufacturing controller consists of a Digital to Analogue Converter with zero order element in series with the machining centre which has a transfer function

)3(

12)(

sssGp

Figure Q5 (c) shows the system. i) Find the sampled-data transfer function, G(z) for the computer

control system. The sampling time, T, is 0.5 seconds. (8 marks)

ii) Find the steady-state error for the computer control system, if the system subjects a step input.

(3 marks)

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Figure Q5 (c) Total 25 marks


Q6 A translational mechanical system is shown in Figure Q6.

Output

- +

Input

Page 8 of 18


Figure Q6 A Translational Mechanical System

(a) Derive the differential equations describing the behaviour of the system. (8 marks)

(b) Select the state variables and transfer the differential equations obtained from Q6(a) above to the relevant first-order differential equations. (2 marks)

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

(9 marks)

Question Q6 continues overleaf



d) Briefly explain the following three approaches for the analysis and design of closed loop control systems:

C1

C2

M2

M1

K2

Y2

Y1

F

Page 9 of 18


i) The Laplace transfer function

ii) The frequency responses technique iii) The state space technique

(6 marks)

Total 25 marks

END OF QUESTIONS

Page 10 of 18


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 11 of 18


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

Re

16f

g2d

fLv4h

2

f

Page 12 of 18


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 13 of 18


1000

gQHp

RRt60

NT

R

RL

uL2F

t

V

rV

4

2

4

1

2

1

2n

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

Page 14 of 18


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)

(for an impulse input) Second-order systems

dtr = 1/2 dtp =

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

(2

ts = n

4 d = n(1-2)

PID Controller GPID = Kp + Ki/s + Kds

)/()1

()(

t

sso eGt

inoono

no b

dt

d

dt

d

22

2

2

2

22

2

2)(

)()(

nn

no

i

o

ss

b

s

ssG

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Page 16 of 18


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Page 18 of 18


DIMENSIONS FOR CERTAIN PHYSICAL QUANTITIES

Quantity Symbol Dimensions

Quantity Symbol Dimensions

Mass m M Mass /Unit

Area m/A 2 ML -2

Length l L Mass moment ml ML

Time t T Moment of

Inertia I ML 2

Temperature T θ - - -

Velocity u LT -1 Pressure /Stress

p /σ ML -1T -2

Acceleration a LT -2 Strain τ M 0L 0T 0

Momentum/Impulse mv MLT -1 Elastic

Modulus E ML -1T -2

Force F MLT -2 Flexural Rigidity

EI ML 3T -2

Energy - Work W ML 2T -2 Shear

Modulus G ML -1T -2

Power P ML 2T -3 Torsional

rigidity GJ ML 3T -2

Moment of Force M ML 2T -2 Stiffness k MT -2

Angular momentum - ML 2T -1 Angular stiffness

T/η ML 2T -2

Angle η M 0L 0T 0 Flexibiity 1/k M -1T 2

Angular Velocity ω T -1 Vorticity - T -1

Angular acceleration

α T -2 Circulation - L 2T -1

Area A L 2 Viscosity μ ML -1T -1

Volume V L 3 Kinematic Viscosity

τ L 2T -1

First Moment of Area

Ar L 3 Diffusivity - L 2T -1

Second Moment of Area

I L 4 Friction

coefficient f /μ M 0L 0T 0

Density ρ ML -3 Restitution coefficient

M 0L 0T 0

Specific heat- Constant Pressure

C p L 2 T -2 θ -1

Specific heat- Constant volume

C v L 2 T -2 θ -1

Note: a is identified as the local sonic velocity, with dimensions L .T -1

Documents

UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING · PDF filePage 3 of 18 School of Engineering BEng (Hons) Mechanical Engineering Semester 1 Examination 2017/2018 Advanced Thermofluids &