PREDICTING TURBULENT FLOW IN A STAGGERED TUBE

MOHD ADIB MUIZZUDDIN BIN MOHLIS

Laporan ini dikemukakan sebagai

Memenuhi sebahagian daripada syarat penganugerahan

Ijazah Sarjana Muda Kejuruteraan Mekanikal (Termal-Bendalir)

Fakulti Kejuruteraan Mekanikal

Universiti Teknikal Malaysia Melaka

September 2007

‘Saya/Kami* akui bahawa telah membaca

karya ini dan pada pandangan saya/kami* karya ini

adalah memadai dari segi skop dan kualiti untuk tujuan penganugerahan

Ijazah Sarjana Muda Kejuruteraan Mekanikal (Termal-Bendalir)’

Tandatangan :…………………………………..

Nama Penyelia I:………………………………..

Tarikh :………………………………………….

Tandatangan:……………………………………

Nama Penyelia II:………………………………

Tarikh:………………………………………….

i

Saya akui laporan ini adalah hasil kerja saya sendiri kecuali ringkasan dan

petikan yang tiap-tiap satunya saya telah jelaskan sumbernya”

Tandatangan :……………………………..

Nama Penulis :……………………………

Tarikh :……………………………………

ii

ACKNOWLEDGEMENT

Alhamdulillah, thanks to ALLAH because I have completed my Projek

Sarjana Muda 1 without facing any major problem.

First and foremost I would like to deliver my deep appreciation and thankful

my supervisor which is my Heat Transfer Subject lecturer, Encik Shamsul Bahari

Bin Azraai for being such a great mentor to me. Much thank and gratitude to Encik

Ahmad Kamal Bin Mat Yamin, Mechanical Engineering supervisor for Projek

Sarjana Muda, for his good concern. I also would like to thanks my family for

encourage and motivate me during this period of industrial training. Besides that I

also would like to thank them for financial support.

Lastly, thanks to Faculty of Mechanical Engineering which has gave an

opportunity to discover Mechanical Engineering Field. I hope this report will be used

by other students as a reference for their project.

iii

ABSTRACT

This report is about predicting turbulent flow in a staggered tube using

Computational Fluid Dynamic software developed by Ansys which is the CFX.

Either CFX, there are many non computational dynamic methods that can predict the

heat transfer and flow characteristic such experimental and analytical method. But

using Computer Fluid Dynamic software can save time and cost because only virtual

model were create and simulate. The aims of this study are to predict the fluid flow

and heat transfer characteristic in a staggered tube air and water as the fluid. The

flow and heat transfer characteristic of a staggered tube a nearly the same of a single

cylinder/tube. The first row characteristic is usually the same as a single tube. But for

the second row and so on, the characteristic are depends on the rows that’s come

first. For a single tube actually there are two boundary layers which occur at front of

the tube and the back of the tube. Laminar boundary layer always developed at the

front while turbulent at the back. Several geometrical parameters have been defined

according to the previous research (journals) done in order to design the staggered

tube geometry. The other parameters such as the fluid velocity and temperature are

also defined according to the previous research. With these parameters a simulation

can be made using CFX. There are several process in CFX which are the CFX Pre-

processing, CFX solver and CFX post processing. The results obtain are in terms of

velocity, temperature and pressure profile. From the investigation lower value of

pitch used will results better heat transfer rate. When the pitch value is decrease, the

pressure drop will rise and thus will increase the heat transfer rate. In engineering

application higher pressure drop value will result higher power required to move the

fluid through the tube bank.

iv

ABSTRAK

Laporan ini menceritakan tentang meramal dan mentafsir aliran bergelora di

dalam tiub yang disusun secara berperingkat dengan menggunakan perisian

pengkomputeran aliran dinamik iaitu Ansys CFX. Selain CFX, terdapat kaedah-

kaedah lain yang boleh meramal dan mentafsir pemindahan haba dan sifat aliran

seperti kaedah pengujian dan analitikal. Tetapi dengan menggunakan kaedah

pengkomputeran aliran dinamik, masa dan kos dapat dijimatkan dan dikurangkan

berbanding dengan menggunakan dua kaedah yang disebut tadi. Ini adalah kerana

hanya model maya saja yang dicipta dan di kaji. Tujuan laporan ini adalah untuk

meramal dan mentafsir sifat aliran dan pemindahan haba didalam tiub berperingkat

dengan menggunakan air dan udara sebagai medium aliran. Sebenarnya sifat aliran

dan pemindahan haba didalam tiub berperingkat adalah hampir menyamai dengan

tiub tunggal. Ini adalah kerana pada barisan pertama sifatnya adalah seperti aliran

tunggal. Pada barisan kedua dan seterusnya sifatnya adalah bergantung kepada

barisan yang datang dahulu. Untuk tiub tunggal, terdapat dua lapisan sempadan yang

terbentuk di hadapan tiub dan dibelakang tiub. Lapisan laminar selalunya terbentuk

dihadapan manakala lapisan bergelora terbentuk di belakang. Beberapa parameter

geometri telah ditentukan berdasrkan kajian yang telah dijalankan oleh pengkaji-

pengkaji untuk mereka geometri tiub. Terdapat juga parameter lain yang telah di

tentukan seperti halaju bendalir dan suhu yang juga berdasrkan jurnal. Dengan

parameter-parameter ini simulasi dapat dilakukan dengan menggunakan CFX.

Terdapat beberapa process didalam CFX seperti CFX pra-proses, CFX penyelesai

dan CFX selepas proses. Keputusan yang diperolehi adalah didalam profil halaju,

suhu dan tekanan. Berdasarkan simulasi yang telah dijalankan, didapati nilai pitch

yang rendah akan meningkatkan kadar pemindahan haba. Tetapi apabila nilai pitch

berkurang, kejatuhan tekanan akan meningkat dan seterusnya meningkatkan kadar

pemindahan haba. Didalam aplikasi kejuruteraan, nilai kejatuhan tekanan yang tinggi

akan menyebabkan lebih banyak kuasa yang diperlukan untuk menggerakkan cecair

melalui tiub-tiub tersebut.

v

TABLE OF CONTENT

CHAPTER TITLE PAGE

PENGAKUAN

ACKNOWLEDGEMENT

ABSTRACT

ABSTRAK

TABLE OF CONTENT

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

LIST OF ABBREVIATONS

i

ii

iii

iv

v

viii

ix

xi

xiii

CHAPTER I INTRODUCTION 1

1.1 Predicting Turbulent in a Staggered Tube

1.2 Objective

1.3 Scope

1.4 Problem Statements

1

2

2

2

CHAPTER II LITERATURE REVIEW 4

2.1 Introduction 4

2.2 Computational Fluid Dynamic 5

2.3 Flow Across Cylinder 6

2.31 Drag Force 7

2.32 Correlation for Average Heat Transfer 9

2.4 Factors that Affect the Heat Transfer and Flow

Characteristic across a Cylinder

10

2.41 Boundary Layer 11

vi

CHAPTER TITLE

2.42 Flow Separation

PAGE

11

2.43 Adverse Pressure Gradient 11

2.44 Wake 12

2.45 Reynolds Number 12

2.5 Flow across Tube Bank 13

2.51 Heat Transfer Coefficient

2.6 Predicting the heat transfer and flow characteristic in a

staggered tube by Previous Researchers

2.61 Numerical/CFD simulation in a staggered tube

2.62 Analytical approach

15

16

17

21

CHAPTER III METHODOLOGY 25

CHAPTER IV

3.1 Introduction

3.2 Typical Stage of CFD

3.3 Steps to Generate CFD Simulations using Ansys CFX

3.4 Ansys Workbench

3.41 Geometry

3.42 Meshing

3.5 CFX Pre-Processing

3.51 Type of Simulation

3.52 Domain

3.53 Boundary Condition

3.54 Solver Control

3.6 CFX Solver

3.7 CFX Post Processing

RESULTS AND DISCUSSIONS

4.1 Temperature Profile

4.2 Velocity Profile

4.3 Pressure Profile

4.4 Velocity Vector and Streamline

25

25

26

27

27

29

31

31

32

32

33

33

33

34

34

39

42

47

vii

CHAPTER V CONCLUSION 50

viii

LIST OF TABLES

TABLE TITLES PAGE

2.1 Parameters used by Incropera et al for staggered

tube bank.

23

2.2 (a) Comparison of results for compact tube bank 24

2.2 (b) Comparison of results for wide tube bank

24

ix

LIST OF FIGURES

FIGURES

NO

TITLES PAGE

1.1 Fluid flow through a staggered a tube 3

2.1 (a) Points that are arranged in staggered 5

2.1 (b) points that are arranged in inline 5

2.1 (c) Isometric view of a staggered tube 5

2.1 (d) Top view of a staggered tube 5

2.2 Cylinder in cross Flow 6

2.3 Velocity profile indicating flow separation on a

cylinder in cross flow

7

2.4 Drag corfficients for circular cylinder and sphere in

cross flow

8

2.5 Correlation of heating and cooling for flow across

cylinder

9

2.6 Schematic of a tube bank in cross flow (staggered

arrangement)

14

2.7 The arrangements for aligned and staggered 14

2.8 Flow conditions for aligned and staggered tubes 16

2.9 Computational grid for tandem cylinder 18

2.10 Boundary conditions by E. Buyruk 19

2.11 Schematic of inline arrangement 21

2.12 Schematic of staggered arrangement 21

2.13 Control volume used by Khan et al for prediction of

heat transfer from tube bank

22

3.1 (a) Tube diameter, LS and TS value for pitch 2.0 28

3.1 (b) Tube diameter, LS and TS value for pitch 1.8 28

3.1 (c) Tube diameter, LS and TS value for pitch 1.6 28

3.2 The container dimension 29

x

3.3 The mesh obtained 30

3.4 The inflation used 30

3.5 Pre processing 31

3.6 Boundary conditions 32

4.1 (a) Temperature contour for pitch 1.6 with velocity of air at 2 m/s 35

4.1 (b) Temperature contour for pitch 1.6 with velocity of air at 10 m/s 36

4.1 (c) Temperature contour for pitch 2 with velocity of air at 2 m/s 36

4.2 (a) Graph of heat transfer against Reynolds Number for air 37

4.2 (b) Graph of heat transfer against Reynolds Number for water 38

4.3 (a) Graph of Nusselt Number against Reynolds Number for air 39

4.3 (b) Graph of Nusselt Number against Reynolds Number for water 39

4.4 (a) Velocity contour for pitch 1.6 with velocity of air at 2 m/s 41

4.4 (b) Velocity contour for pitch 1.6 with velocity of air at 10 m/s 41

4.4 (c) Velocity contour for pitch 2.0 with velocity of air at 2 m/s 42

4.5 (a) Pressure contour for pitch 1.6 with velocity of air at 2 m/s 43

4.5 (b) Pressure contour for pitch 1.6 with velocity of air at 10 m/s 44

4.5 (c) Temperature contour for pitch 2.0 with velocity of air at 2 m/s 44

4.6 Pressure drop agains Reynold Numbers graph for air 45

4.7 Pressure drop against Reynolds Number graph for water 46

4.8 (a) Heat transfer against pressure drop for air 46

4.8 (b) Heat transfer against pressure drop for water 47

4.9 Velocity vector for pitch 1.6 with air velocity at 10 m/s 48

4.10 Streamline for pitch 1.6 with air velocity at 10 m/s 49

xi

LIST OF SYMBOLS

u = Free stream velocity, m/s

V = Upstream velocity, m/s

ReD = Reynolds Number (for cylinder)

DC = Drag Coefficient

h = Heat Transfer Coefficient

D = Tube Diameter, m

K = Thermal Conductivity, W/mC.ºC

v = Kinematic Viscosity, 2 1m s

Pr = Prandtl Number

C, 1C m, n = Constant

DNu = Nusselt Number

s = Mean Fluid Velocity, m/s

= Fluid Density, 3kgm

= Dynamic Fluid Viscosity, 2Nsm

L = Characteristic Length, m

TS = Transverse Pitch, m

LS = Longitudinal Pitch, m

DS = Diagonal Pitch, m

T = Ambient Temperature, °C

1A = Length from tangent of two tubes in transverse, m

2A = Length from tangent of two tubes in diagonal, m

T = Temperature, °C

L = Length, m

lmT = Log Mean Temperature Different

N = Total Number of tubes in Bank

xii

w = Wall Shear Stress, 2Nm

wT = Wall Temperature, °C

Q = Heat Transfer Rate, W

= Distance Normal to and Measured From Surface of Tube,m

u = s-component of Velocity in Boundary Layer, m/s

= - component of Velocity in Boundary Layer, m/s

maxu = Mean Velocity in the Minimum Free Cross Section of the

Control Volume, m/s

xiii

LIST OF ABBREVATIONS

CFD = Computational Fluid Dynamic

REV = Representative Elementary Volume

RSM = Reynolds Stress Model

RMS = Root Mean Square

2D = Two Dimension

3D = Three Dimension

CAD = Computer Aided Design

FEM = Finite Element Method

DNS = Direct Numerical Simulation

LES = Large Eddy Simulation

1

CHAPTER I

INTRODUCTION

This chapter will explained briefly about predicting turbulent in a staggered

tube using computational fluid dynamic, the objective of this study, scopes and the

problem statements.

1.1 Predicting Turbulent in a Staggered Tube

The earliest numerical solution in studying steady flow across a circular

cylinder was reported during 1933. Since that early work, many studies of flow and

heat transfer across tubes and within tube banks have been done using CFD

(Computational Fluid Dynamic) software. Heat transfer and flow characteristic

prediction across cylinder are important in various engineering aspect and have been

presented in many related engineering application. This have been an active research

because it have many benefits in practical of heat exchanger tube bundles, flow

across overhead cables and for nuclear power plant cooling system.

To obtain the flow characteristic and heat transfer around tube bundles,

Navier Stokes and Energy equation can be used to calculate them. Better degree of

approximation can be obtain depending on many factors including the solution

method, mesh size, boundary condition and the stability and convergence criteria.

Although there are many experiment and data that had been done and collected by

previous researchers, it is yet possible to get a clear view about the flow and heat

transfer process across tube bundles because of its complex geometry and there are

many large number of parameter involved.

In this study, CFD software will also be used to predict the heat transfer and

turbulent flow across staggered tubes. CFD simulation for turbulence is harder to

2

make rather than laminar flow because the turbulence flow field are always unsteady

(random, swirling, vertical structures called turbulence eddies). There are many ways

to solve the CFD calculation such as Finite Element Method, Direct Numerical

Simulation and Large Eddy Simulation. Finite Element Method will be used for the

CFD calculation in this study because the CFD software chooses are based on the

FEM.

1.2 Objective

The objectives of this study are to predict the heat transfer and flow

distribution of a staggered tube.

1.3 Scopes

Design CFD staggered tube geometry.

Simulate air and water through an array of heated staggered tube.

1.4 Problem Statement

To simulate a flow across staggered tube, many parameters have to be

decided. These parameters will affect the simulation results. There several

parameters that must be considered for predicting turbulent in a staggered tube which

are:

Longitudinal and transverse pitch

Reynolds Number

Thermal and wall boundary condition

Surface Roughness (in this study it is consider a smooth tube)

3

Number of rows

Fluid properties

Tube diameter

Figure 1.1 shows the fluid flow through a staggered tube. The flow enters at exactly

normal to the tube. The detailed boundary condition will be shown in methodology

chapter.

Figure 1.1: Fluid flow through a staggered a tube

Flow In

Flow Out

4

CHAPTER II

LITERATURE REVIEW

This chapter will explain in detail about the flow across cylinder and tube

bank and the formula used. It also includes the previous studies that have been done

by previous researchers.

2.1 Introduction

Staggered tube is a bundle/bunch of tube which are arranged in staggered.

From dictionary it stated that staggered means not arranged consecutively or in a

straight line [1]. This mean that the tube is not arranged in inline. The succeeding

row of tubes is offset so as not to be directly behind the preceding row of tubes in the

airflow direction. This type of arrangement is similar to atom arrangement which is

the lattice arrangement. This will increases thermal capacity over an inline pattern at

the cost of a higher air friction. Figure 2.1 (a) and 2.1 (b) shows the examples of

staggered and inline arrangement using point. The isometric and top views of

staggered tube are shown in Figure 2.1 (c) and (d).

5

(a) (b)

(c) (d)

Figure 2.1: Shows the points that are arranged in staggered (a) and inline (a)

while (c) and (d) shows the isometric view and top view of a

staggered tube

Staggered tube is important in many industrial applications. As mentioned in

the introduction chapter, it can be used in nuclear power plant, steam generation in a

boiler and coil of an air conditioner. Many studies have been done because of its

potential and importance in heat exchanger. In this study the staggered tube bank will

be study numerically using CFD package software Ansys CFX.

2.2 Computational Fluid Dynamic

CFD is a computational technology that enables you to study the dynamics of

things that flow [2]. CFD is one of the branches of fluid mechanic that uses

numerical method and algorithm to solve problems that interconnect with fluid flow

[3]. With CFD people can build a virtual model that represents the system and device

that he/she wants to study. Then fluid flow physic and chemistry can be applied to it

and computers will perform the millions of calculation that required in the simulation

[2].

6

2.3 Flows across Cylinder

Heat transfer occurs by a cylinder cross flow is as important as heat transfer

through flat plates and inside a tube. The heat transfer characteristic is affected by the

development of boundary layer on the cylinder. However pressure gradient is

important in the analysis and must be included because it influences the boundary

layer velocity profile. It also causes a separated flow region that develops at the back

of the cylinder when the free stream velocity, u is large. From figure, the fluid is

bought to the forward stagnation point with increasing in pressure. From the

boundary layer theory the pressure through the boundary layer is constant at any

position of the body. But for cylinder case, from the forward stagnation point the

pressure will decrease due to increasing of x which is the streamline coordinate and

this condition will develop a boundary layer because of the favorable pressure

gradient (dp/dx<0). The upstream velocity, V and u is differ from each other. The

free stream velocity depends on the distance x (refer Figure 2.2) from the stagnation

point. When free stream velocity equals to zero, which is at the stagnation point the

adverse pressure gradient (dp/dx>0) will make the fluid accelerates and reaches a

maximum velocity when dp/dx=0 (at the symmetrical line of the cylinder). Note that

the pressure will start increasing when it reaches the starting of the back of the

cylinder and the fluid will decelerate due to the adverse pressure gradient. During

this situation, the velocity is maximum and the fluid will start decreasing. As the

fluid decelerates, the velocity gradient at the surface becomes zero. Figure 2.2 and

Figure 2.3 show the flow across cylinder and its velocity profile that shows the

velocity separation [10 and 11].

Figure 2.2: Cylinder in cross Flow

7

Figure 2.3: Velocity profile indicating flow separation on a cylinder in cross flow

This makes the fluid near to the surface does not have enough momentum to

overcome the pressure gradient and will result a separation point (0[ / ] 0yu y ).

Separation point is a condition where the boundary layer detaches from the surface

and wake is occurring in the downstream region. Reverse phenomena of the fluid

occurs as it pass the separation point [10].

Usually laminar boundary layer will develop at the front of the cylinder and

turbulent boundary layer will develop at the back of the cylinder [11]. But there is

also possibility that a transitional boundary layer will develop in between these two

boundary layers and this is depends on the Reynolds Number. If the 5Re 2 10D x the

boundary layer remains laminar but when 5Re 2 10D x , transition boundary layer

occurs and the separation will be delayed [10].

2.31 Drag Force

This repeatedly process will influence the drag force to the cylinder. It has

two components which are:

Friction Drag (due to boundary layer surface shear stress).

Form or Pressure Drag (due to pressure differential in flow direction

because of the wake formation)

8

A drag coefficient can be defined as:

2( / 2)

DD

f

FC

A V

(2.1)

Figure 2.4 shows the drag coefficient versus Reynolds number graph for flow across

circular cylinder and sphere for comparison.

Figure 2.4: Drag corfficients for circular cylinder and sphere in cross flow

This drag coefficient is a function of Reynolds Number. For Re 2D the

separation effect can be neglect because friction drag has dominated the conditions.

From the graph above if the ReD is low, the DC will become high. This is because at

low Red , there is no flow separation and all the drag is resulted from viscous friction.

If it is high the DC will reduce due to boundary layer transition (delay separation)

and that’s why will reduce the extent of wake region. The turbulent separated flow

region happens when the ReD is greater than 1000. The boundary layer becomes

fully turbulent is when the ReD is approximately equivalent to 510 . This will result in

a steeper velocity profile and extremely late flow separation [10 and 11].

9

2.32 Correlation for Average Heat Transfer

There are actually 3 correlation equations for average heat transfer of flow across

cylinder. The equations are stated below.

1. The first equation is the easiest to use from a computational standpoint.

Figure 2.5 shows the correlated data of a number of investigators for heating

and cooling of air by Mc Adams [11].

d

f

hDNu

k

Reu D

v

Figure 2.5: Correlation of heating and cooling for flow across cylinder [10]

The resulting correlation for average heat transfer is:

1/3Pr

n

d f

f f

u DhDNu C

k v

(2.2)

The subscripts f means that all of the properties used are evaluated at film

temperature. The Prandtl number is constant at all data because it is not

included in correlation plot. The constant values of different Reynolds

number used for equation (2.2) can be found in J.P Holman heat transfer book

[11].