# MGII 885 PEC

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THERMAL
-
FLUID SYSTEMS MODELLING I

STUDY GUIDE FOR

MGII 885 PEC

*MGII885PEC*

FACULTY OF ENGINEERING

ii

Study guide compiled by:

Prof PG Rousseau

Dr M van Eldik

Edited

nn
.

#

Page layout by
Elsabe Strydom
,
g
raphikos
.

Printing arrangements and distribution by Department Logistics (Distribution Centre).

Printed by Nashua Digidoc Centre 018 299 2827

20
1
1

edition. Date of revision 20
1
1
.

North
-
West University, Potchefstroom Campus.

No part of this book may be reproduced in any form or by any means without written
permission from the publisher.

iii

MODULE CONTENTS

Module information

................................
................................
................................
.....................
iv

A word of welcome

................................
................................
................................
.....................
iv

Lecturers’ contact information

................................
................................
................................
....
iv

Teaching assistant’s contact information

................................
................................
...................
iv

Module description and rationale

................................
................................
...............................
iv

Module outcomes

................................
................................
................................
.......................

v

What are thermal
-
fluid systems?

................................
................................
................................

v

Course overview

................................
................................
................................
.........................

v

Scheduling

................................
................................
................................
................................
..
vi

Assessment

................................
................................
................................
................................
vi

Study material and other requirements

................................
................................
......................
vi

Warning against plagiarism

................................
................................
................................
.......

vii

Study unit 1

Introduction to system simulation

................................
........................

9

Study unit 2

Integrated system simulation
................................
...............................

11

Study unit 3

Fundamentals of thermal
-
fluid simulation

................................
.........

19

Study unit 4

-
state pipe flow simulation

................................
.......................

21

Study unit 5

-
state heat exchanger simulation

..................

23

Study unit 6

Transient simulation
................................
................................
..............

29

iv

MODULE INFORMATION

A WORD OF WELCOME

Welcome to Thermal
-
Fluid Systems Modelling

I. I trust that you will enjoy this post
-
course and that it will help prepare you for the proper application of fundamental principles in
the modelling and design of industrial thermal
-
fluid systems.

LE
CTURERS’ CONTACT INF
ORMATION

Name:

Prof Pieter G Rousseau

Telephone:

082 4529290

e
-
mail:

pgr@mtechindustrial.com

Name:

Dr Martin van Eldik

Telephone:

082 9272065

e
-
mail:

martin.vaneldik@nwu.ac.za

TEAC
HING ASSISTANT’S CON
TACT INFORMATION

Name:

Joe
-
Nimique Cilliers

Telephone:

082 529 0788

e
-
mail:

12430080@nwu.ac.za

MODULE DESCRIPTION A
ND RATIONALE

The aim of the module is to present the underlying principles and concepts on which
thermal
-
fluid simulation and design software, such as Flownex, is based. In the process the
student should also gain enhanced understanding of the practical implications of the
fundamental theoretical principles.

This is not a software user course but rather an

extension and enrichment of the knowledge
required to apply modelling and simulation in the design process.

In this regard the student will be guided through the development of mathematical models
and integrated cycle simulations with the aid of the gen
eric Engineering Equation Solver
(EES) software package. Students will be required to successfully complete several
thermal
-
fluid modelling assignments.

v

MODULE OUTCOMES

After completion of this course the student must be able to:

Integrate fundamental
knowledge of thermodynamics, fluid mechanics and heat
transfer with specialised techniques required to simulate thermal
-
fluid systems for both

Apply higher level engineering synthesis skills and specialised software

tools to create
mathematical models with the appropriate degree of complexity that can be used in the
simulation and design of thermal
-
fluid components and systems.

WHAT ARE THERMAL
-
FLUID SYSTEMS?

The terms ‘thermal
-
fluid systems’ refer to all systems of
which the performance is governed
by the principles of thermodynamics, fluid mechanics and heat transfer.

These systems are typically made up of components such as fans, pumps, compressors,
turbines, heat exchangers, reactors and valves, all connected via
pipes or ducts. The
working substances are fluids, which include liquids, gasses and gas
-
liquid two
-
phase flows.

Practical examples of thermal
-
fluid systems are air conditioners, refrigerators, heat pumps,
power plants, reactors, gas turbine engines as we
ll as water and gas pipelines and
reticulation networks.

A working knowledge of the relevant engineering sciences and mathematics is therefore a
pre
-
requisite. This includes the laws of conservation of mass, momentum and energy and
the equations of state
for gasses and liquids, the Darcy
-
Weisbach equation and Moody
diagram for calculating pressure losses in pipes and ducts, the distinction between laminar
and turbulent flow, the distinction between compressible and incompressible flows, the
effectiveness
-
N
TU and LMTD methods for simulating heat exchanger performance as well
as the formulation and physical interpretation of the various non
-
dimensional numbers
including Reynolds, Nusselt and Prandtl.

COURSE OVERVIEW

Study

Unit

1

introduces thermal
-
fluid syste
m simulation. This includes looking at the
distinction between simulation and design, the different levels of complexity of simulation
models, the differences and similarities between the Computational Fluid Dynamics (CFD)
approach versus the so
-
called Sy
stems
-
CFD (SCFD) approach and the generic structure of
mathematical simulation models. It also revisits the fundamental definitions required in the
modelling of thermal
-
fluid systems.

Study

Unit

2

looks at how to construct simulation models for whole inte
grated thermal
-
fluid
plants, without having much detail of the characteristics of each individual component. This
type of simulation is typically used in the concept design phase and is useful for overall
system optimization. It also provides the operati
ng conditions for each of the components in
the system therefore facilitating the detailed design of each individual component.

Study

Unit

3

looks in quite some detail at the derivation of the complete fundamental
conservation laws for the SCFD implementat
ion within stationary inertial frameworks.

Study

Unit

4

addresses the first element of the component characteristic equations, namely
the detailed calculation of pressure drops. It looks at the velocity boundary layer and its
influence on frictional press
ure drop. This is illustrated by applying it to steady
-
state
incompressible and compressible flow through pipes and ducts.

vi

Study

Unit

5

addresses the second element of the component characteristic equations,
namely the detailed calculation of heat trans
fer rates. It looks at the thermal boundary layer
and its influence on convection and diffusion heat transfer characteristics. This is illustrated
-
state heat exchanger operation.

Study

Unit

6

introduces the learner to
the simulation of transient flows. We first look at the
different time
-
wise integration schemes for the conservation equations and then apply it to
some transient thermal
-
fluid system simulation examples.

SCHEDULING

The successful completion of this modul
e will require approximately one man
-
month worth of
effort i.e. 180

hours of study, during a time period of eight calendar weeks. The contact
week will comprise approximately 40

hours. This means that during the other seven weeks
you will have to spend o
n average 20 hours per week on self
-
study and working on
assignments, including preparing for and taking the examination.

ASSESSMENT

You will be required to submit ten assignments. All the assignments must be completed in
your own time and submitted stri
ctly according to the accompanying work schedule, by no
later than 12:00 on the date indicated for submission. Assignments will be graded by the
Teaching Assistant

(TA) and the grades for all your assignments will be averaged to provide
a module participa
tion mark. You must submit all the assignments strictly according to the
work schedule, and obtain a module participation mark of at least 40% in order to gain
entrance to the examination.

The examination will take place in the last week of the eight cale
ndar week period. The
examination will consist of two parts. Part

1 will be closed
-
book and will focus on the theory
and detail information contained in the course notes. Part

2 will be open book and will
consist of actually programming a simulation mod
el on EES for a thermal
-
fluid component or
system.

The final module mark will be the weighted average of the mark achieved in the examination
and the module participation mark, on an 80:20 basis. A sub
-
minimum of 40% must be
achieved in the examination in

order to pass the module. There will be no re
-
examination.

STUDY MATERIAL AND O
THER REQUIREMENTS

This Study Guide and the Course Notes will be your most important sources. For
thermodynamics, heat transfer and fluid mechanics fundamentals you are refe
rred to the
appropriate textbooks that were prescribed for those specific courses in your under
-
years.

extensively in this module. It will be necessary for yo
computer where
you

can run EES while carrying out the homework assignments. You are
expected to master the use of EES on your own and submit several assignments even
before the contact week.

vii

WARNING AGAINST PLAG
IARISM

ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES
.
(UNLESS
EXPLICITLY INDICATED AS GROUP ACTIVITIES)

Copying
of text from other learners or from other sources (for instance the study guide,
prescribed material or directly from the internet) is
not
allowed

only brief quotations are
allowed and then only if indicated as such.

You should
reformulate

existing text and use your
own words
to explain what you have
read. It is not acceptable to retype existing text and just acknowledge the source in a
fo
otnote

you should be able to relate the idea or concept, without repeating the original
author to the letter.

The aim of the assignments is not the reproduction of existing material, but to ascertain
whether you have the ability to integrate existing te
critique of the texts and offer a creative solution to existing problems.

Be warned: students who submit copied text will obtain a mark of zero for the
assignment and disciplinary steps may be taken by the Faculty an
d/or University. It is
also unacceptable to do somebody else’s work, to lend your work to them or to make
your work available to them to copy

be careful and do not make your work available
to anyone!

viii

Study unit 1

9

1

INTRODUCTION TO SYST
EM
SIMULATION

Contents:

1.1.

Simulation versus design

1.2.

Levels of complexity

1.3.

CFD vs SCFD approach

1.4.

Generic structure of simulation model

1.5.

Fundamental definitions

Outcomes:

After completing this study unit you should be able to:

Explain the
difference between simulation and design.

Describe how simulation is used in the design process.

Explain the four levels of complexity of simulation models and provide an example of
each.

Explain the differences and similarities between the CFD and SCFD ap
proaches and
provide examples of where each would be applied in a real
-
world design problem.

Name and briefly describe the four types of equations that make up the generic
structure of a well
-
formulated simulation model.

Know and understand the definitions

of the fundamental properties including static
enthalpy, pressure and temperature, the heat capacities, Mach number and the total
enthalpy, pressure and temperature for incompressible and compressible flows.

Time

The study time proposed for this Study
Unit is 20 hours.

Overview:

Study

Unit

1

introduces thermal
-
fluid system simulation. This includes looking at the
distinction between simulation and design, the different levels of complexity of simulation
models, the differences and similarities between

the Computational Fluid Dynamics (CFD)
approach versus the so
-
called Systems
-
CFD (SCFD) approach and the generic structure of
mathematical simulation models. It also revisits the fundamental definitions required in the
modelling of thermal
-
fluid systems.

Study unit 1

10

Study material.

This unit and the assignment must be completed via self
-
study within the scheduled time set
out in the accompanying work program. Work through the material in the course notes and
make sure that you have reached the outcomes described ab
ove. Following this, complete
the assignment given below. If you have any problems or questions, contact the teaching
assistant.

Assignment 1: Compressible versus incompressible flow

Set up a calculation in EES to illustrate the differences and similariti
es between the
definitions for total pressure in compressible and incompressible flow. Use air at a constant
temperature of 20

C and static pressure of 100

kPa and compare the values of total pressure
for Mach numbers between zero and one.

Present your
results in a concise, but high quality report containing the following:

A listing of your EES program.

An EES plot comparing the two definitions as a function of Mach number.

Study unit 2

11

2

INTEGRATED SYSTEM
SIMULATI
ON

Contents:

2.1.

Simplified conservation laws

2.2.

Simplified component characteristics

2.3.

Programming methodology

2.4.

Brayton cycles

2.5.

Rankine cycles

2.6.

Combined cycles

2.7.

Vapour compression cycles

Outcomes:

After completing this study unit you should be able to:

Formulate
the simplified component characteristic equations for pipes and ducts, heat
exchangers, turbines, compressors, pumps and shaft energy balance.

Develop EES programs to model the integrated system performance of Brayton,
Rankine and vapour compression cycles

based on the simplified component
characteristic models.

Use the integrated simulation models to investigate different system operating points
and extract from it the operational specifications of the different components in the
system.

Time

The study
time proposed for this Study Unit is 60 hours.

Overview:

Study

Unit

2

looks at how to construct simulation models for whole integrated thermal
-
fluid
plants, without having much detail of the characteristics of each individual component. This
type of simu
lation is typically used in the concept design phase and is useful for overall
system optimization. It also provides the operating conditions for each of the components in
the system therefore facilitating the more detailed design of each individual comp
onent.

Study unit 2

12

Study material.

This unit and the assignments must be completed via self
-
study within the scheduled time
set out in the accompanying work program. Work through the material in the course notes
and make sure that you have reached the outcomes desc
ribed above. Following this,

complete the assignment given below. If you have any problems or questions, contact the
teaching assistant.

Assignment 2a: Complex Brayton cycle simulation

The figure below shows the layout of a closed
-
loop, two
-
stage, recuper
ated and inter
-
cooled
Brayton cycle similar to that employed in the PBMR Brayton cycle design. The cycle
employs Helium as the working fluid. The generator, turbine and LP and HP compressors
are all situated on a single shaft. The pressure ratios of the

LP and HP compressors are
exactly the same.

The heat source is a nuclear Pebble Bed Reactor

(PBR). From the reactor the hot Helium
gas flows to the turbine

(TRB) that drives the Low Pressure Compressor

(LPC), High
Pressure Compressor

(HPC) and Generator

(G). From the turbine the gas flow to the low
pressure side of the recuperator heat exchanger

(RXLP) then through the Pre
-
Cooler

(PC).
The Inter
-
Cooler

(IC) is situated between the two compressor stages. After final
compression the gas flows through the

high pressure side of the recuperator

(RXHP) where
it picks up heat that would have been rejected at the PC, before it flows back to be reheated
in the PBR.

The following fluid properties are given as fixed values for Helium:

k
J/kgK,
kJ/kgK,
kJ/kgK and
.

The following boundary values are given:

kPa,
ºC and the cooling water temperature fed to the pre
-

and
inter
-
cooler is
ºC.

Study unit 2

13

The following component characteristics are given:

The efficiency of both compressors is
.

The efficiency of the turbine is
.

The effectiveness of all the heat exchangers is
.

The pressure loss factor for all pipes is
.

The pressure loss factor for all heat exchangers is
.

The pressure loss factor through the reactor is
.

The reactor power is
MW.

The mechanical efficiency of the shaft is
.

Your assignment is to do the following:

Set up a complete i
ntegrated system simulation model for this cycle using EES.

Calculate the optimum value for the compressor pressure ratio

(
) (i.e. the same
value for both the LP and HP compressors) where the cycle thermal efficiency

(
) has
a maximum value.

For this optimum pressure ratio determine the required Helium mass flow rate

(
) and
the cycle thermal efficiency.

For this optimum pressure ratio use the built
-
in functionality is EES to draw t
he
temperature vs specific entropy and pressure vs specific enthalpy diagrams for the
cycle.

Present your results in a concise, but high quality report containing the following:

A listing of your EES program.

A listing of your solution and array tables fro
m EES.

A graph showing the cycle thermal efficiency as a function of the compressor pressure
ratio.

The T
-
s and p
-
h diagrams.

Study unit 2

14

Assignment 2b: Complex Rankine cycle simulation

The figure below shows the layout of a three
-
stage reheated and regenerative Rank
ine cycle,
similar to that of a typical ESKOM coal
-
fired power station.

Saturated liquid water at low temperature and pressure enters the Low Pressure Pump

(LPP)
from where it is pumped to the Low Pressure Heater

(LPH). In the LPH the water is mixed
wit
h steam from the outlet of the Intermediate Pressure Turbine

(IPT). The mixture is
pumped via the Intermediate Pressure Pump

(IPP) to the Intermediate Pressure Heater

(IPH)
where it is again mixed with steam from the outlet of the High Pressure Turbine

(H
PT). From
the IPH the water is pumped via the High Pressure Pump

(HPP) to the Boiler

(B) where the
water is heated, evaporated and superheated before entering the HPT.

At the outlet of the HPT the fraction of steam that is not bled off to the IPH is ret
urned to the
boiler and re
-
heated in the Re
-
Heater

(RH) to the same temperature as the HPT inlet steam.
From the RH the steam flows to the IPT. From there the fraction not bled off to the LPH
flows to the Low Pressure Turbine

(LPT) where it is expanded a
nd the condensed in the
Condenser

(CD) with the aid of cooling water supplied by the cooling towers. From the
condenser the saturated liquid flows back to the LPP.

The built
-
in steam fluid properties designated “
Steam_IAPWS”
in EES must be used for this
a
ssignment.

The following boundary values are given:

The high, intermediate and low pressure levels are 160

bar, 39

bar and 2.7

bar
respectively.

The maximum steam temperature is 540

ºC and the condensing temperature is 33

ºC.

The fraction of steam bled off

to the regenerative feed water heaters is 6.7% of the flow
rates leaving the HPT and IPT respectively.

The total power supplied by the generator (after subtracting the power required to drive
the feed water pumps) must be 600

MW.

Study unit 2

15

The following component
characteristics are given:

The efficiency of all the turbines is
.

The efficiency of the pumps is
.

The pressure losses in the all pipes, the boiler, re
-
heater, condenser and the heaters
are negligible.

The mechanical losses in the shaft is negligible.

Your assignment is to do the following:

Set up a complete integrated system simulation model for this cycle using EES.

Calculate the required water mass flow rate

(
) through the bo
iler and the cycle
thermal efficiency

(
).

Use the built
-
in functionality is EES to draw the T
-
s and p
-
h diagrams for the cycle.

Present your results in a concise, but high quality report containing the following:

A listing of your

EES program.

A listing of your solution and array tables from EES.

The T
-
s and p
-
h diagrams.

Assignment 2c: Heat Pump cycle simulation

The figure below shows a heat pump cycle that will be used to heat water from temperature

to

in the condenser while it cools dry air from

to
.

Refrigerant gas at low pressure and temperature is compressed through the compressor to a
high pressure and high temperature.

From there heat

(
) is given off in the condenser heat
exchanger to the medium being heated. As heat is given off, the superheated refrigerant
vapour cools down to the point where it becomes saturated vapour. The temperature at

this
point is called the condensing temperature

(
). From there the refrigerant condenses until it
becomes saturated liquid. As more heat is given off the refrigerant liquid is sub
-
cooled. The
Study unit 2

16

temperature difference between the

saturated liquid point and the outlet of the condenser is
referred to as the degree of sub
-
cool

(
).

From the outlet of the condenser the refrigerant moves through the expansion valve where it
is throttled to a low pressure and co
rresponding low temperature in a constant enthalpy
process. The refrigerant enters the evaporator as a two phase mixture. In the evaporator
heat exchanger heat

(
) is picked up by the refrigerant from the medium being cooled. Th
e
refrigerant evaporates until it reaches the saturated vapour point. The temperature at this
point is referred to as the evaporating temperature

(
). As more heat is picked up, the
refrigerant gas is superheated to a higher temp
erature. The temperature difference between
the outlet of the evaporator and the saturated vapour point is referred to as the degree of
superheat

(
).

In this exercise we will discretize the evaporator and condenser heat exchanger
s into a
number of increments. In this way we will be able to see how the temperature profiles
develop along the heat exchangers and also start to get an idea of the size of heat
exchanger required in each case.

The figure below shows a schematic of the T
-
s diagram for the sample heat pump cycle that
we will simulate. It shows the refrigerant, water and air temperatures as well as the
increments of the two heat exchangers.

The two
-
phase region of the evaporator is divided into eight equal enthalpy increm
ents and
the superheat region into two equal enthalpy increments. These increments are numbered 1
to 10 and the nodes that separate then are numbered 0 to 10.

The superheat region of the condenser is divided into three equal enthalpy increments,
numbered
21 to 23, and the two
-
phase region into six equal enthalpy increments, numbered
24 to 29. The sub
-
cooled region of the condenser consists of a single increment, numbered
30. The nodes separating the condenser increments are numbered 21 to 30.

We will now

systematically set up the simulation model for the heat pump that utilizes
refrigerant R407c with the following boundary values:

The condensing temperature is 50

ºC and the evaporating temperature is 15

ºC.

The degree of sub
-
cool will be 8

ºC and the supe
rheat 12

ºC.

The heating capacity of the heat pump will be 100

kW.

Study unit 2

17

The following component characteristics are given:

The isentropic efficiency of the compressor is
.

The pressure and heat losses in the all pipes are negligible.

Your assignment is to do the following:

Set up a complete integrated system simulation model for this cycle using EES.

Calculate the required refrigerant mass flow rate

(
) and the COP of the cycle.

The dry air is cooled from 30

ºC

to 20

ºC while the water is heated from 25

ºC to 50

ºC.
What are the required air and water mass flow rates?

Use the built
-
in functionality is EES to draw the T
-
s and p
-
h diagrams for the cycle,
including the air and water temperatures on the T
-
s diagra
m.

Assuming that for each increment in both the condenser and evaporator you can write
the required incremental

value as

with

the incremental
value of heat transfer and

and

as the average fluid temperatures on the hot and
cold sides respectively, calculate what the total required UA values will be for the
condenser and evaporator heat exchangers respectively.

Present yo
ur results in a concise, but high quality report containing the following:

A listing of your EES program.

A listing of your solution and array tables from EES.

The T
-
s and p
-
h diagrams.

Study unit 2

18

Study unit 3

19

3

FUNDAMENTALS
OF
THERMAL
-
FLUID SIMULATION

Contents:

3.1.

Control volume definition

3.2.

Conservation of mass

3.3.

Conservation of momentum

3.4.

Conservation of energy

3.5.

Summary

Outcomes:

After completing this study unit you should be able to:

Recognise the differential form of each of
the fundamental conservation equations,
explain the assumptions under which they are valid and describe the physical meaning
of each of the terms.

Integrate each of the fundamental conservation equations in differential form over a
control volume with fini
te length to obtain the integral form.

Recognise the integral form of each of the fundamental conservation equations, explain
the assumptions under which they are valid and describe the physical meaning of each
of the terms.

Write down the definitions of t
otal enthalpy, total temperature and total pressure for
both incompressible and compressible flows.

Time

The study time proposed for this Study Unit is 10 hours.

Overview:

Study

Unit

3

looks in quite some detail at the derivation of the complete fundamental
conservation laws for the SCFD implementation within stationary inertial frameworks. This is
necessary in order to build suitable simulation models.

Study material

This unit will be

introduced during the contact week. However, assignments must be
completed via self
-
study within the scheduled time set out in the accompanying work
program. Work through the material in the course notes and make sure that you have
reached the outcomes
described above. Following this, complete the assignment given
below. If you have any problems or questions, contact the teaching assistant.

Study unit

3

20

Assignment 3: Compressible flow theorem

Prove that for compressible flow
.

Stud
y unit 4

21

4

-
STATE PIPE FLOW
SIMULATION

Contents:

4.1.

Conservation of mass

4.2.

Conservation of momentum

4.3.

Conservation of energy

4.4.

Component characteristics

4.5.

Pipe simulation case study

Outcomes:

After completing this study unit
you should be able to:

Apply the correct formulations of the detailed component characteristic equations to
calculate the pressure drop in pipes and ducts.

Write down the definition of the Reynolds number and explain its practical significance.

Set up a si
mple discretized pipe simulation in EES to calculate the pressure and
temperature distributions along the length of the pipe.

Develop EES programs to model the detailed pressure distributions in pipes and ducts
for both incompressible and compressible stea
dy
-
state flows.

Time

The study time proposed for this Study Unit is 30 hours.

Overview:

Study

Unit

4

addresses the first element of the component characteristic equations, namely
the detailed calculation of pressure drops. This is illustrated by applying it to steady
-
state
incompressible and compressible flow through pipes and ducts.

Study material

This

unit will be introduced during the contact week. However, assignments must be
completed via self
-
study within the scheduled time set out in the accompanying work
program. Work through the material in the course notes and make sure that you have
reached
the outcomes described above. Following this, complete the assignments given
below. If you have any problems or questions, contact the teaching assistant.

Study unit 4

22

-
state pipe flow

The figure above shows a pipe that transport
s chilled water down a mine shaft. Set up and
EES model to simulate the flow through the pipe using 10 increments of equal length and
determine:

The mass flow rate.

The outlet water temperature.

Present your results in a concise, but high quality report c
ontaining the following:

A listing of your EES program.

A listing of your solution and array tables from EES.

Graphs showing the temperature and pressure distributions along the length of the
pipe.

-
state pipe flow

The f
igure above shows a pipe that transports compressed air over a long distance. Set up
and EES model to simulate the flow through the pipe using 10 increments of equal length
and determine:

The mass flow rate.

The outlet air temperature

in a concise, but high quality report containing the following:

A listing of your EES program.

A listing of your solution and array tables from EES.

Graphs showing the temperature and pressure distributions along the length of the
pipe.

Study unit 5

23

5

INTRODUCTION TO
-
STATE HEAT
EXCHANGER SIMULATION

Contents:

5.1.

Conservation equations

5.2.

Component characteristics

Outcomes:

After completing this study unit you should be able to:

Write down the definition of the
overall heat transfer coefficient as it is applied to model
any heat exchanger increment.

List the thermal resistances that make up the overall heat transfer coefficient.

Discuss the different approaches to the modelling of the heat transfer rate between
d
ifferent fluid streams i.e. (i)

based on the difference between average fluid
temperatures, (ii)

based on the LMTD and (iii)

the effectiveness
-
issues such as the similarities, differences and relationship between the methods,
s and limitations of each method as well as its practical applicability.

Explain the definition of the overall surface efficiency and fin efficiency and how and
where it is applied in practice.

Write down the definitions of the terms used in the effectiven
ess
-
NTU method.

Select the appropriate effectiveness
-
NTU relationship to employ for any given heat
exchanger geometry.

Explain the characteristics of the most important effectiveness
-
NTU relationships and
what the impact thereof is on heat exchanger design
.

Derive and discuss (from Newton’s law of cooling and Fourier’s law) the conservation
equation for convection and diffusion heat transfer from the thermal boundary layer.

Write down the definitions of the Nusselt and Prandtl numbers and explain the practi
cal
significance of each.

Recognise and correctly apply the Nusselt number correlations for pipe flow and
complex heat transfer surfaces.

Explain the definition of the Darcy
-
Weisbach and Fanno friction factors and how and
where it is applied in practice.

Apply the correct formulations of the detailed component characteristic equations to
calculate the heat transfer rates in pipes and heat exchangers.

Develop EES programs to model the detailed pressure and temperature distributions in
pipes, ducts and heat
exchangers for both incompressible and compressible
-
state flows.

Study unit 5

24

Time

The study time proposed for this Study Unit is 40 hours.

Overview:

Study

Unit

5

addresses the second element of the component characteristic equations,
namely the detailed calculation of heat transfer rates. It looks at the thermal boundary layer
and its influence on convection and diffusion heat transfer characteristics. This i
s illustrated
-
state heat exchanger operation.

Study material

This unit will be introduced during the contact week. However, assignments must be
completed via self
-
study within the scheduled time set out in the accompanying

work
program. Work through the material in the course notes and make sure that you have
reached the outcomes described above. Following this, complete the assignment given
below. If you have any problems or questions, contact the teaching assistant.

Ass
ignment 5a: Discretized tube
-
in
-
tube heat exchanger simulation

The figure above shows a schematic of a counter flow, concentric tube heat exchanger that
must be designed to heat water with

kJ/kgK,

kg/
m
3
,

Ns/m
2
,

kW/mK and the
from 20 to 80

ºC using hot oil with

kJ/kgK,

kg/m
3
,

Ns/m
2
,

kW/mK and the Prandtl number is equal
to 103. The oil is supplied at 160

ºC and discharged at 140

ºC. The thin
-
walled inner tube
has a diameter of 20

mm and the outer tube has a diameter of 30

mm. The outer tube is
totally insu
lated from the surroundings. The heat exchanger must be designed to provide
3

kW of heating to the water.

Set up a simulation model in EES for the heat exchanger discretized in 10 increments
along its length.

Calculated what the required length of the hea
t exchanger will be.

Plot the temperature and pressure distribution along the length of the heat exchanger.

If fouling of the heat exchanger surface only takes place on the water
-
side where the
wall temperature rises above 60

ºC, what length of the heat ex
changer will be affected?

Present your results in a concise, but high quality report containing the following:

A listing of your EES program.

A listing of your solution and array tables from EES.

The temperature and pressure distribution plots.

Study unit 5

25

Assignment

5b: PWR fuel rod simulation

The figure below shows a typical layout of a fuel rod/element and fuel assembly of a
Pressurised Water Reactor

(PWR). The reactor core is made up of several fuel assemblies
arranged together and submerged in a pool of speciall
y treated light water. The water is
circulated through the core with circulation pumps and flows from the bottom to the top
through the gaps in between the fuel rods.

Figure
1

PWR fuel rod and fuel assembly.

Study unit 5

26

A
schematic of the fuel rod lattice layout is shown below.
The outer diameter of the fuel rod
is typically
mm and the pitch between the centres of the fuel rods is
mm. The length of a single fuel rod is
m.

Although there are now
physical boundaries between the water flowing around each fuel rod, a representative flow
channel can be drawn around each rod such as the one shown in the dashed square.

Figure
2

Fuel rod lattice layout.

Figure
3

shows a cross
-
section of a fuel rod. It consists of a UO
2

fuel compact surrounded
by a Zircaloy cladding with a very thin gap
in between that is initially filled with Helium gas.
The fuel compact diameter is

. The
thermal conductivity of the fuel compact material is
kW/mK and that of the
Zircaloy is
kW/mK.

Figure
3

Fuel rod cross
-
section.

Study unit 5

27

You are asked to set up a calculation/simulation of the flow over a single representative fuel
rod and flow channel in order
to calculate the temperature and pressure distribution in the
water for ten increments of equal length along the full height of the rod. Also, you must
calculate the following temperatures within the fuel rod material for each of the ten
increments: the c
entre of the fuel assembly
, the temperature of the outer surface of
the fuel compact
, three additional temperatures equally spaced in between the centre
and the outside surface of the fuel compact namel
y
,

and

as well as
the inner surface temperature of the cladding

and the outer surface temperature of
. The
effects of radiation heat transfer through the gap as well as axial
heat conduction within the fuel rod can be ignored.

The total power generated within the fuel compact is 100

kW and the power generation
varies along the length of the fuel rod in a cosine

shape as shown in
Figure
4
. The heat
generated in each of the ten increments along the length of the rod must be distributed
between the five representative temperat
ure nodes in the fuel compact on pro
-
rata basis
according to the volume of fuel material contained in the control volume represented by each
temperature node.

Figure
4

Cosine shaped power generation profile along the length of th
e fuel rod.

The water mass flow rate across a single fuel rod is
kg/s and the water inlet
temperature and pressure is

C and
kPa respectively. The Nusselt
number for turbulent flow parallel to a rod bundle can be calculated from
. The relative roughness of the outside surface of the
.

Study unit 5

28

Do the following:

Set up a d
etailed discretized simulation model in EES for one fuel rod with its
representative flow channel with ten increments along the total length.

Calculate the water inlet and outlet temperatures and pressures of each increment.

Calculate the values of seven r
epresentative temperatures within the fuel rod cross
-
section as well as the average water temperature for each of the ten increments.

Plot the radial temperature distribution profiles for each of the ten increments along the
length of the fuel rod.

Plot th
e axial temperature distribution profiles along the length of the fuel rod for each
of the seven representative temperatures within the fuel rod cross
-
section as well as
the average water temperature.

Submit your EES program together with the two temperatu
re distribution plots.

Study unit 6

29

6

TRANSIENT SIMULATION

Contents:

6.1

Conservation of mass

6.2

Conservation of momentum

6.3

Conservation of energy

6.4

Component characteristics

6.5

Turbo machine dynamics

Outcomes:

After completing this study unit you should be able to:

Name and discuss the three most important time
-
wise integration schemes for the
numerical solution of transient differential equations. Address issues such as the
numerical stability and
accuracy.

Integrate each of the conservation equations for transient flow over a discrete time step
of length

to obtain the integral form.

Write down the transient diffierential equation that accounts for a fluid mass enclosed in

a reservoir, the thermal mass of heat exchanger material the inertia of rotating
components and integrate it over a discrete time step of length

to obtain the integral
form.

Set up a simulation in EES for a transient event for a

fluid mass enclosed in a reservoir,
a heat exchanger increment and for a rotating machine with inertia to calculate the
variations in parameters with time given fluctuating boundary conditions.

Time

The study time proposed for this Study Unit is 20 hours

Overview:

Study

Unit

6

introduces the learner to the simulation of transient flows. We first look at the
different time
-
wise integration schemes for the conservation equations and then apply it
some transient thermal
-
fluid system simulation examples.

Study unit 6

30

Study material

This unit will be introduced during the contact week. However, assignments must be
completed via self
-
study within the scheduled time set out in the accompanying work
program. Work through the material in the course notes and make sure tha
t you have
reached the outcomes described above. Following this, complete the assignments given
below. If you have any problems or questions, contact the teaching assistant.

Assignment 6a: Transient reservoir simulation

A reservoir with an internal volume

of 10

m
3

initially contains dry air at 100

kPa and 20

ºC.
The reservoir is perfectly insulated from the environment surrounding it. Additional dry air
can be fed into the reservoir at a given mass flow rate of

while air can al
so be extracted
independently at a rate of
. The temperature of the air fed into the reservoir is designated

and the reservoir contains an internal heat source designated
. Se
t up a transient
simulation model of the reservoir that models the first hour of a transient with time step sizes
of
seconds. Simulate the following cases and plot pressure versus time and
temperature versus time graphs for each
case:

1.

ºC,
kg/s,

kg/s and
kW.

2.

ºC,

kg/s,

kg/s and

kW.

3.

ºC,

kg/s,

kg/s and

kW.

4.

ºC,

kg/s,

kg/s and

kW.

5.

ºC,

kg/s,

kg/s and

kW.

6.

ºC,

kg/s,

kg/s a
nd

kW.

Present your results in a concise, but high quality report containing the following:

A listing of your EES program.

The pressure and temperature transient plots for each of the cases above.

Study unit 6

31

Assignment 6b: Transient heat
exchanger

A counter flow, concentric tube heat exchanger like the one shown schematically above must
be designed to heat 0.012

kg/s of water with

kJ/kgK,

kg/m
3
,

Ns/m
2
,

kW/mK and the

from 20

ºC using 0.06

kg/s of hot
oil with

kJ/kgK,

kg/m
3
,

Ns/m
2
,

kW/mK and the
Prandtl number is equal to 103. The oil is supplied at 160

ºC. The inner tube has an inner
diameter of 20

mm and wall thickness of 5

mm while the outer tube has a diameter of
40

mm. The properties of the wall material are

kJ/kgK,

kg/m
3
,

kW/mK. The outer tube is totally insulated from the surroundings. The length of the
heat exchanger is 1

m.

Set up a simulation model in EES for the heat exchanger with one in
crement only.

-
state heat duty will be.

If the oil temperature is suddenly decreased to only 100

ºC, plot the change in the
outlet temperatures of the water and oil together with the wall temperatures on the
primary and secondary s
ides respectively as a function of time.

Present your results in a concise, but high quality report containing the following:

A listing of your EES program.

The temperature transient plots.