tw40 university of bolton school of ......tw40 university of bolton school of engineering beng...

TW40

UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING

BENG (HONS) IN MECHANICAL ENGINEERING

SEMESTER 1EXAMINATION 2015/2016

ADVANCED THERMOFLUIDS & CONTROL

SYSTEMS

MODULE NO: AME6005

Date: Wednesday 13 January 2016 Time: 10.00 – 1.00

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

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School of Engineering BEng (Hons) Mechanical Engineering Semester 1 Examination 2015/2016 Advanced Thermofluids & Control Systems Module No: AME6005

Q1 (a) Fluid is moving through a pipe. The velocity profile at some section is

shown in Figure Q1a and is given mathematically as:

2

2

r4

d

4u

Where u = velocity of fluid at any position r, = a constant, =

viscosity of fluid, d = pipe diameter and r = radial distance from

centreline. Calculate:

i. The shear stress at the wall of the pipe due to fluid. (6 marks)

ii. The shear stress at a position r = d/4 (4 marks)

And

iii. If the given profile persists a distance L along the pipe, what drag

is induced on the pipe by the fluid in the direction of flow over this

distance. (5 marks)

Figure Q1a

Question 1 continued overleaf

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Question 1 continued

(b) A shaft 70mm in diameter is being pushed at a speed of 400 mm/s

through a bearing sleeve 70.2mm in diameter and 250mm long. The

clearance is filled with oil with kinematic viscosity of 0.005 m2/s and

specific gravity 0.9. Calculate the force exerted by the oil on the shaft.

(10 marks)

Total 25 marks

Q2 (a) Show from first principles that the change of entropy for a gas is

𝑆2 - 𝑆1 = ∁𝑉 𝐿𝑛 𝑇2

𝑇1 + R 𝐿𝑛

𝑉2

𝑉1

Use dQ = du + dw

du = ∁𝑉 d T and dw = pdv (12 marks)

(b) Water at 20oC flows at a rate of 0.05 m3/s in a 20cm diameter cast iron

pipe. Calculate the head loss per kilometre of the pipe. Take the

kinematic viscosity of water at: 20oC = 1 x 10-6 m2/s. The Ks value for

cast iron = 0.12mm.

Use the attached Moody diagram (13 marks)

Total 25 marks

Please turn the page

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Q3 (a) The wall shear stress τ

w in a boundary layer is assumed to be a

function of stream velocity U, boundary layer thickness δ, local turbulence velocity u′, density ρ, and local pressure gradient dp/dx. Using (ρ, U, δ) as repeating variables, rewrite this relationship as a dimensionless function. (15 marks)

b) A Rankine cycle works between 40 bar and 400℃ at the boiler exit and 0.035 bar at the condenser. Sketch the cycle and calculate the cycle efficiency.

Assume isentropic expansion and ignore the energy term at the feed pump.

(10 marks)

Total 25 marks

Q4 A solar tracking system shown in Figure Q4, in which a PID controller is used to control the system. The system responses for a unit step input are required as:

The maximum overshoot is less than 10%

The settling time is 50% less than the closed loop system without the PID controller

The steady-state error is 0.

If the solar system Gp(s) = 100

(𝑠+3)(𝑠+6),

(a) Evaluate the performances of closed loop system (ξ, ωn,

Percentage Overshoot, ts and steady-state error) without the PID

controller to determine how much improvement is required.

(8 marks)


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(b) Determine the PID parameters KP, Ki, and Kd.

(12 marks)

(c) If a velocity feedback is introduced into Figure Q4, draw a block

diagram with the velocity feedback and explain the effects on a

control system of including the velocity feedback. (5 marks)

Total 25 marks

Q5 A simplified driverless vehicle model is shown in Figure Q5, in which

the computer performs the function of controller by using Global Positioning System (GPS) information to generate input commands for the vehicle.

(a) Determine the range of sampling interval, T, which will make the

feedback control system stable, and the range that will make it unstable. (8 marks)

(b) For a unit step input and a unit ramp input, find the steady-state

error for the feedback control system. (8 marks)


Figure Q4 A Solar Tracking System

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(c) If the controller has a 16 bit Analogue to Digital Converter with

the signal range between -10 Volt to +10 Volt:

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

(ii) What integer number represented a value of 5 Volts?

(2 marks)

(iii) What voltage does the integer 1000 represent?

(2 marks)

(iv) What voltage does 1011010110110011 represent?

(3 marks)

Total 25 marks

Please turn the page

Figure Q5 A Simplified Driverless Vehicle Model

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Q6 A simple mechanical system shown in Figure Q6. K1 and K2 are the

spring stiffness, C is the viscous damping coefficient, and M1 and M2

are the masses for Mass 1 and Mass 2. The input to the system is the

Force F and the outputs are the velocities dy1/dt and dy2/dt, and

displacements y1 and y2.

(a) Develop the system’s differential equations (5 marks)

(b) Determine the state variables dy1/dt, dy2/dt, y1 and y2 (2 marks)

Figure Q6 A Mechanical System

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

(10 marks)



(d) Explain the following two approaches for the analysis and design of closed loop control systems and give two advantages and two disadvantages for each of the technique :

The frequency responses technique

The state space technique (8 marks)

Total 25 marks

END OF QUESTIONS

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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

1 -n

V P - V P =W 2211

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s = sf + xsfg

v = x Vg

hm w - Q...

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

sCDFD2u

2

1

suFL2

LC 2

1

)( gZPds

dS p

L

pDQ

128

4

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gD

L

Rh f

2

v64 2

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

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1000

gQHp

RRt60

NT

R

RL

uL2F

t

V

rV

4

2

4

1

2

1

2n

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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( / tssO eG (for a unit step input)

)1( / tssO 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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