Report containing secret of universe

Numerical analysis of wake flow on heated

cylinder

A PROJECT REPORT

Submitted by

DULARISH K A 312211114029

INTI SANDEEP 312211114043

in partial fulfillment for the award of degree of

BACHELOR OF ENGINEERING

in

MECHANICAL ENGINEERING

SSN COLLEGE OF ENGINEERING, CHENNAI -603110

ANNA UNIVERSITY: CHENNAI 600 025

APRIL 2015

ANNA UNIVERSITY: CHENNAI 600 025

ii

BONAFIDE CERTIFICATE

Certified that this project report Numerical analysis of wake flow of

heated cylinder is the bonafide work of Dularish K A, Inti

Sandeep who carried out the project work under my supervision.

SIGNATURE

Dr. V.E ANNAMALAI

HEAD OF THE DEPARTMENT

Mechanical Engineering,

SN College of Engineering,

OMR, Kalavakkam- 603110.

SIGNATURE

Dr. S. SOMA SUNDARAM

ASSOCIATE PROFESSOR

Mechanical Engineering

SSN College of Engineering,

OMR, Kalavakkam- 603110.

SUBMITTED FOR THE VIVA VOCE EXAM HELD ON: ___________

INTERNAL EXAMINER EXTERNAL EXAMINER

iii

ACKNOWLEDGEMENT

We are grateful to our Principal Dr. S. Salivahanan for

providing us a constructive environment for carrying

out our project.

We sincerely thank our Head of the Department,

Dr. V. E. Annamalai for giving us permission to carry

out our numerical analysis project.

We would like to express our gratitude to our guide

Dr. S.Soma Sundaram, for his valuable guidance and

support throughout the period of this project work.

iv

ABSTRACT

The thermal effects of the wake flow behind a heated

cylinder operating in mixed convection region is

studied numerically and is been compared with

experimental study. Water with constant temperature

flows under gravity from the top over a heated bluff

body maintained at a constant temperature. By adjusting

the surface temperature of solid, the corresponding

Richardson number is varied. This variation is observed

for different cross sectional bluff bodies. The optimal

cross section for which there is minimum heat transfer

and the one for which there is maximum heat transfer is

determined. The analysis was done on a CFD software

to determine the pattern of velocity and temperature

distribution. The study revealed that cross-section shape

changes the flow pattern significantly for the same area.

Heat transfer is maximum for circular cross section and

minimum in equilateral triangle . The change in

velocity pattern due to change of Richardson number is

negligible for a cross-section shape considered.

v

TABLE OF CONTENTS

CHAPTER NO. TITLE PAGE NO.

ABSTRACT iv

LIST OF FIGURES vii

LIST OF SYMBOLS x

1. Introduction 1 1.1 Wake Flow 2 1.2 Vortex shedding 3 1.3 Reynolds Number 4 1.4 Turbulent flow 4 1.5 Nusselts number 5

2. Literature Survey 6

3. Procedure 9

4. Design Calculations 13 4.1 Time Step Calculation 13 4.2 No. of Time Steps 13 4.3 Geometry 13 4.4 Mesh process 14 4.5 Assumptions 15 4.6 Boundary Conditions 15

vi

5. Numerical Results 16

5.1 Circular cross section cases 16 5.2 Equilateral triangle cross section cases 22 5.3 Hexagon cross section cases 24 5.4 Inverse equilateral triangle cross section case 26 5.5 Square cross section cases 28

6. Conclusions 33

vii

List of Figures & Tables

Figure 1.1 Wake flow

Figure 3.1 Temperature grid study

Figure 3.2 Velocity grid study

Figure 3.3 Temperature temporal study

Figure 3.4 Velocity temporal study

Figure 4.1 Geometry of circular cross section in cylindrical pipe

Figure 4.2 Mesh Region

Figure 4.3 Prism layer and wake refinement

Table 5.1 Tabulation of cases considered

Figure 5.1 Velocity magnitude plot for circular cross section

Figure 5.2 Temperature magnitude plot for circular cross section






Figure 5.8 Velocity magnitude plot for circular cross section

Figure 5.9 Temperature magnitude plot for equivalent triangle cross

section

viii

Figure 5.10 Velocity magnitude plot for equivalent triangle cross

section

Figure 5.11 Temperature magnitude plot for equivalent triangle cross

section

Figure 5.12 Velocity magnitude plot for equivalent Triangle cross

section

Figure 5.13 Temperature magnitude plot for hexagon cross section

Figure 5.14 Velocity magnitude plot for hexagon cross section

Figure 5.15 Temperature magnitude plot for hexagon cross section

Figure 5.16 Velocity magnitude plot for hexagon cross section

Figure 5.17 Temperature magnitude plot for inverse equivalent

triangle cross section

Figure 5.18 Velocity magnitude plot for inverse equivalent triangle

cross section

Figure 5.19 Temperature magnitude plot for inverse equivalent

Triangle cross section

Figure 5.20 Velocity magnitude plot for inverse equivalent triangle

cross section

Figure 5.21 Temperature magnitude plot for square cross section

Figure 5.22 Velocity magnitude plot for square cross section

Figure 5.23 Temperature magnitude plot for square cross section

Figure 5.24 Velocity magnitude plot for square cross section

Figure 5.25 Velocity with respect to position graph for circular cross

section

ix

Figure 5.26 Temperature with respect to position graph for circular

cross section

Figure 5.27 Temperature with respect to position graph for different

geometries

Figure 5.28 Velocity with respect to position graph for different

geometries

Table 5.2 Parameters along the probe

x

LIST OF SYMBOLS, ABBREVIATIONS AND NOMENCLATURE

Re - Reynolds Number (no unit)

Gr - Grashof Number (no unit)

Ri - Richardson Number (no unit)

Pr - Prandtl Number (no unit)

St - Strouhl Number (no unit)

Nu - Nusselt Number (no unit)

f - Frequency (hertz)

D - Diameter Of Pipe (metre)

V - Velocity Of Fluid (m/s)

T - Time Period ( seconds )

Chapter 1

Introduction

An understanding of the flow around a bluff body is of great

importance owing to its fundamental nature as well as its many

related engineering applications. A circular cylinder is the most

commonly studied bluff body. Despite its simple shape, a circular

cylinder generates a wake that is dynamically complex. By varying

the Reynolds number, a variety of flow patterns and vortex shedding

characteristics in the wakes of circular cylinders have already been

observed. The wake behaviour behind a heated cylinder is physically

more complicated owing to the thermal effects added to the viscous

phenomena. Heat transfer from a heated cylinder to the surrounding

fluid can be either forced convection, mixed convection or pure free

convection, depending on the ratio between the thermally induced

buoyancy force and the inertial force, characterized by the Richardson

number (Ri = Gr/Re2, where Gr is the Grashof number and Re is the

Reynolds number). In forced convection (Ri >1), where the flow inertial force is negligible, heat

transfer is a function of Grashof number (Gr) and Prandtl number

(Pr). In mixed convection, both forced convention and free convection

are important, and heat transfer is a function of Grashof number (Gr),

Reynolds number (Re) and Prandtl number (Pr) as well as the

approaching forced flow direction. Despite the fact that mixed

convection around bluff bodies is of great importance for various

engineering applications such as electronics cooling, micro heat

exchangers and fuel cells, the thermal effects on the wake flow

behaviour behind a bluff body in the mixed convection regime have

received little attention compared to those in the forced or free

Page | 2

convection. When a heated cylinder operates in the mixed convection

regime, the thermally induced buoyancy force plays an important role

in the flow behaviour in the wake. For a horizontally placed heated

cylinder, the free-stream approach flow can be either horizontal,

vertically upward or vertically downward, they are called horizontal

cross-flow, parallel flow and contra-flow arrangements based on the

angle between the approach flow direction and the thermally induced

buoyancy force acting on the fluid surrounding the heated cylinder.

1.1 Wake Flow The flow downstream of a body immersed in a stream or the flow

behind a body propagating through a fluid. Wakes are narrow

elongated regions; filled with large and small eddies. The wakes

eddies of a bridge pier immersed in a river stream, or of a ship

propelled through the water, are often visible on the surface. On

windy days, similar wakes form downstream of smoke stacks or other

structures, but the eddies in the air are not visible unless some smoke

or dust is entrained in them.

Turbulence in the wake of bluff bodies consists of all sizes of eddies,

which interact with each other in their unruly motion. Yet, out of this

chaos emerges some organization, whereby large groups of eddies

form a well-ordered sequence of vortices. The sense of rotation of

these vortices alternates and their spacing is quite regular. As a result,

they can drive a structure that they encounter or they can exert on the

body that created them a force alternating in sign with the same

frequency as that of the formation of the vortices. Such forces can

impose on structures unwanted vibrations which often lead to serious

damage. Flow induced forces can be catastrophic if they are in tune

with the frequency of vibration of the structure. Wakes are sustained

for very large distances downstream of a body. Ship wakes retain

their turbulent character for miles behind a vessel and can be detected

by special satellites hours after their generation. Similarly

Page | 3

condensation in the wake of aircraft sometimes makes it look like a

narrow braided cloud, traversing the sky.

Figure 1.1

1.2 Vortex Shedding

Vortex shedding is an oscillating flow that takes place when a fluid

such as air or water flows past a bluff (as opposed to streamlined)

body at certain velocities, depending on the size and shape of the

body. In this flow, vortices are created at the back of the body and

detach periodically from either side of the body. The fluid flow past

the object creates alternating low-pressure vortices on the downstream

side of the object. The object will tend to move toward the low-

pressure zone. If the bluff structure is not mounted rigidly and the

frequency of vortex shedding matches the resonance frequency of the

structure, the structure can begin to resonate, vibrating with harmonic

oscillations driven by the energy of the flow. This vibration is the

cause of the singing of overhead power line wires in a wind, and the fluttering of automobile whip radio antennas at some speeds.

Tall chimneys constructed of thin-walled steel tube can be sufficiently

flexible that, in air flow with a speed in the critical range, vortex

shedding can drive the chimney into violent oscillations that can

damage or destroy the chimney. These chimneys can be protected

Page | 4

from this phenomenon by installing a series of fences (sometimes

called strakes or spoilers) at the top and running down the exterior of

the chimney for approximately 20% of its length. The fences are

usually located in a helical pattern.

The fences prevent strong vortex shedding with low separation

frequencies. The optimal pitch for vortex shedding is a 5D pitch (5 x

the diameter of the stack).

1.3 Reynolds Number

The Reynolds number is defined as the ratio of inertial forces

to viscous forces and consequently quantifies the relative importance

of these two types of forces for given flow conditions. Reynolds

numbers frequently arise when performing scaling of fluid dynamics

problems, and as such can be used to determine dynamic

similitude between two different cases of fluid flow. They are also

used to characterize different flow regimes within a similar fluid, such

as laminar or turbulent flow

Laminar flow occurs at low Reynolds numbers, where viscous forces

are dominant, and is characterized by smooth, constant fluid motion.

Turbulent flow occurs at high Reynolds numbers and is dominated by

inertial forces, which tend to produce chaotic eddies, vortices and

other flow instabilities.

1.4 Turbulent flow

Turbulent flow, type of fluid (gas or liquid) flow in which the fluid

undergoes irregular fluctuations, or mixing, in contrast to laminar

flow, in which the fluid moves in smooth paths or layers. In turbulent

flow the speed of the fluid at a point is continuously undergoing

changes in both magnitude and direction. The flow of wind and rivers

is generally turbulent in this sense, even if the currents are gentle. The

air or water swirls and eddies while its overall bulk moves along a

specific direction.

Page | 5

Most kinds of fluid flow are turbulent, except for laminar flow at the

leading edge of solids moving relative to fluids or extremely close to

solid surfaces, such as the inside wall of a pipe, or in cases of fluids of

high viscosity (relatively great sluggishness) flowing slowly through

small channels. Common examples of turbulent flow are blood flow

in arteries, oil transport in pipelines, lava flow, atmosphere and ocean

currents, the flow through pumps and turbines, and the flow in boat

wakes and around aircraft-wing tips.

1.5 Nusselt Number

Page | 6

Chapter 2

Literature Survey

2.1 The Thermal Effects on the Wake Flow behind a

Heated Circular Cylinder Operating In the Mixed

Convection Regime[1]

The thermal effects on the wake flow were investigated

experimentally. The experiment was conducted such that water flows

in a channel over a heated cylinder which is maintained at a particular

temperature. By controlling the temperature, Richardson number is

varied from 0 to 1.04 resulting the heat transfer change from forced

convection to buoyancy induced free convection. Molecular Tagging

Velocimetry & Thermometry (MTV &T) technique is used to

visualize velocity and temperature distribution. By varying

Richardson number, significant changes in the characteristics of the

system such as recirculation distance, wake closure length, vortex

shedding process. It was observed that when Richardson number is

increased , the usual Karman vortices at the two sides of the bluff

body is delayed and replaced by Kelvin-Helmholtz like vortex

structures and drag coefficients were found to be increased due to

thermally induced flow. The average Nusselt number were found to

be linearly decreasing with increasing Richardson numbers. A

numerical study yielded similar results in predicting wake vortex

characteristics and flow pattern

Page | 7

2.2 Passive Control of wake flow behind a

circular cylinder by parallel dual plates[2]

This is a numerical study on the effect of control device, consisting of

two plates placed parallel to the wake centreline, on wake

characteristics with the objective of wake stabilization. Two parallel

plates were placed behind the circular bluff body over which flow

takes placed in a low Reynolds number regime. Extensive studies

were performed by varying the angle of the plates and the number of

plates. There was significant difference in the wake parameters by

introducing plates at the rear of a bluff body and for thorough wake

stabilization, the length of the plate must be 5 times that of bluff body

diameter. The coefficient of drag experience change as high as 23%

close to L/D ratio of 1.5. Depending of the angle of the plates, the

wake regime can be classified into three regimes, when the angle of

the plates increased there was a decrease in coefficient of drag. In this

paper, two mechanisms for the control of dual plates is suggested.

First is the stabilization of free shear layer fluctuation and the other

one is the basal cavity effect which accounts for pressure

redistribution upon the base surface region.

2.3 Heat Transfer From A Cylinder In The Wake

Flow[3] In this work, the effect of obstacle size and the shape on the heat

transfer characteristics is studied. An additional cylinder is placed

downstream of the bluff body and convective characteristics are

determined. Conductive and radiation heat transfer is considered

negligible. Lumped heat capacitance method is used in determining

heat transfer coefficients. For every obstacle shape and size, the effect

of spacing between obstacles and location of obstacles relative to one

another is studied. It was observed that heat transfer did not vary

Page | 8

significantly at lower Reynolds number but when Reynolds number

was higher, heat transfer was significantly higher. For higher

Reynolds number, the larger the obstacle size, the higher was the

average Nusselt number. When the obstacle was present just behind

the circular object, the obstacle had a negative effect on the heat

transfer, but for square cross section object, heat transfer showed an

improvement.

2.4 Dependence of flow classification on the

Reynolds number for a two-cylinder wake[4]

This is a study on aerodynamic interference between multiple

structures. Flow behind two staggered cylinders is more complicated

than with single cylinder configuration. Moreover, flow

characteristics depend on angle between the flow direction and the

line joining two cylinders and the pitch distance between two

cylinders. The experiments were performed in a wind tunnel of

section 2.4m x 0.6m x 0.6m in which uniform flow takes place. Two

hotwires are used to simultaneously measure velocity fluctuation.

Flow modes are divided based on the values of pitch ratio and angle.

An increase in Reynolds number reduces boundary layer thickness,

causes a shift in separation point towards forward stagnation point,

increases separation angle and decrease in vortex formation length. It

was found that transition from one flow mode to another or the border

of flow regime solely dependent on the variation of Reynolds number.

Page | 9

Chapter-3

Procedure

The analysis is attempted in a CFD software, and the final results

are to be compared with experimental results. The properties of

the fluid and temperature are considered same as experiment

performed.

The problem is modelled as per the experiment and suitable

boundary conditions and initial conditions are set. The suitable

options in the models set are chosen.

Grid independence and temporal independence studies are done in

order to determine base size and time step size. Too low base

sizes and time step sizes would yield accurate results but consume

unaffordable computational time. Large base and time step sizes

would take less computational time but with a compromise on

accuracy. Therefore, base size and time step sizes must be chosen

such that they give results of sufficient accuracy with affordable

computational time.

Page | 10

Figure 3.1

Figure 3.2

Page | 11

After finalizing with base size and time step size, the analysis of six

cases are performed. The temperature and velocity plots are extracted

from scalar scene and to be compared with the plots from the

experiment.

Figure 3.3

Page | 12

Figure 3.4

Additionally, the ideal geometries for minimum and maximum heat

transfer are to be determined. So the other geometries that are

considered include Equilateral Triangle, Inverse Equilateral Triangle,

Square, Hexagon.

Page | 13

Chapter 4

Design calculations

4.1 Time step calculation:

For flow over cylinders, strouhal number can be approximated to 0.2

St = f D / V

Where f is the frequency of vortex shedding.

By substituting D = 4.76mm & V = 0.026m/s

We get f =1.09 Hz, Time period = 0.917s.

So, we choose a standard time step close to 0.917s as 0.1s.

Temporal independence study is done by varying time period below

0.1s.

4.2 Number of time steps:

We know distance of fluid travel = 200mm,

Velocity of fluid = 0.026m/s

Therefore, time taken for fluid to travel = 7.611s

For more accurate values, we take time as 20s.

For t = 0.1, No: of time steps: 20/0.1 = 200

For t = 0.01, No: of time steps: 20/0.01 = 2000

4.3 Geometry

Figure 3.1

Page | 14

4.4 Mess process

Trimmer type elements are utilised in building up the geometry.

Additionally, prism layer and wake refinement are implemented

around the bluff body so as to obtain more accurate results.

Arbitrarily base size of 0.005m, which is close to the diameter of the

cylinder is chosen. In the wake refinement region, the size is 6% of

base size. Grid independence study is performed by decreasing the

base sizes below 0.005m. Due to the capability of the computers we

possess, base sizes below 0.003m could not be meshed.

Figure 5.2

Prism Layer and wake refinement:

Figure 5.3

Page | 15

4.5 Assumptions

The analysis is symmetric along the cross section. Hence two-

dimensional analysis is sufficient. The fluid used is water which is

incompressible and of constant density. Owing to Reynolds number

being very low, laminar flow is assumed. Gravity function is turned

on, as the water flows under gravity. Segregated flow is assumed.

4.6 Boundary conditions

The temperature of the water is initially set as 24C and flows with a

intial velocity of 0.026 m/s from the top edge. The temperature of

bluff body is maintained constant throughout the analysis and depends

on the specific case. The bottom edge of the section is assumed

pressure outlet.

4.7 Converging criteria

Mass balance and enthalpy balance errors are calculated for every

analysis done and made sure whether the errors are within acceptable

limits. Mass balance is the difference between mass entering through

the inlet and mass leaving the outlet. Similarly, enthalpy balance is

the difference between enthalpy of the inlet edge and the enthalpy

through the outer edge

Page | 16

Chapter 5

Numerical Results

Considering for the below cases

Case

no.

Tw (0C) T (

0C) Re Gr Ri

1 24 24.0 135 0 0.00

2 35 24.0 135 3400 0.19

3 42 24.0 135 5600 0.31

4 53 24.0 135 9100 0.50

5 66 24.0 135 13100 0.72

6 85 24.0 135 19100 1.04

Table 5.1

5.1 Circular Cross section cases: Tw =240C

Velocity

Figure 5.1

Page | 17

Temperature

Figure 5.2

Tw =350C:

Temperature

Figure 5.3

Page | 18

Tw =420C:

Temperature

Figure 5.4

Tw =530C:

Temperature

Figure 5.5

Page | 19

Tw =660C:

Temperature

Figure 5.6

Tw =850C:

Temperature

Figure 5.7

Page | 20

Velocity

Figure 5.8

The change in velocity plot for different Richardson numbers is

negligible. As the Richardson number increases, the temperature in

the wake region increases considerably.

A central vertical probe is considered and the velocity and

temperature values are tabulated and analysed for temperature

regainment distance and velocity recirculation distance. The

maximum temperature along the central probe is higher than that of

other shapes under similar condition.

Page | 21

5.2 Equilateral Triangle cross section Tw =240C

Temperature

Figure 5.9

Velocity

Figure 5.10

Page | 22

Equilateral Triangle cross section Tw =850C

Temperature

Figure 5.11

Velocity

Figure 5.12

In case of Equilateral triangle, the wake vortices observed were more

disorder and the peak velocity observed along the centreline is

relatively higher when compared with other shapes. It has the

maximum temperature regainment distance with the value 200%

Page | 23

greater than that of circle and has velocity recirculation distance 31%

lower than that of circle.

5.3 Hexagon cross section Tw =240C

Temperature

Figure 5.17

Velocity

Figure 5.18

Figure 5.13

Velocity

Figure 5.14

Page | 24

Hexagon cross section Tw =850C

Temperature

Figure 5.15

Velocity

Figure 5.16

In case of hexagon, the wake plots are similar to circle but with higher

velocity recirculation and temperature regainment distances. Velocity

Page | 25

recirculation distance is 18% higher than that of circle and

temperature regainment distance is 50% higher than that of circle.

5.4 Inverse equilateral Triangle Tw =240C

Temperature

Figure 5.17

Velocity

Figure 5.18

Page | 26

Inverse equilateral Triangle Tw =850C

Temperature

Figure 5.19

Velocity

Figure 5.20

In case of Inverted Equilateral triangle, the region where buoyancy

forces are predominant is wider when compared to other geometries.

It is interesting to note that the wake vortices formed are exactly

behind the apex of the triangle, but they form behind the other sides

too. Temperature regainment distance is 50% higher than that of

Page | 27

circle and velocity recirculation distance is 31% lower than that of

circle.

5.5 Square cross section Tw =240C

Temperature

Figure 5.21

Velocity

Figure 5.22

Page | 28

Square cross section Tw =850C

Temperature

Figure 5.23

Velocity

Figure 5.24

The temperature plot of Square cross section is similar to that of

circular but the velocity plot differs significantly such that it has the

maximum velocity recirculation distance among all the shapes that

have been studied. Relatively lower values of peak temperature and

peak velocity are observed. The velocity recirculation distance is

37.5% higher than that of circle and temperature regainment distance

is same as that of circle.

Page | 29

Velocity with respect to Position graph for circular cross section

Figure 5.25

Temperature with respect to Position graph for circular cross

section

Figure 5.26

Page | 30

Temperature with respect to Position graph for different

geometrical cross sections:

Figure 5.27

Page | 31

Velocity with respect to Position graph for different geometrical

cross sections:

Figure 5.28

There is no change in the values of velocity observed along the

centreline probe for same cross section. However, for different

geometries, there is a significant change in velocity recirculation

distance and temperature regainment distance. As the Richardson

number increases, the temperature peak increases. The change in

temperature regainment distance can vary as much as 200% and the

change in velocity recirculation distance can vary as much as 100%

Page | 32

Parameters along the probe

Shapes Velocity

Recirculation

Region

Distance

(mm)

Temperature

Regainment

Distance

(mm)

Peak

Temperature

(Deg. C)

Peak

Velocity

(mm/s)

Equilateral

Triangle

11 12 35.5 12.81

Hexagon 19 6 62.47 6.26

Inverted

Equilateral

Triangle

11 6 48.85 8.84

Square 22 4 40 6.8

Circle 16 4 72.5 7.97

Table 5.2

Page | 33

Chapter 6

Conclusions

It was observed that there was no velocity distribution along the

centreline for the same cross section. The decreasing order of

maximum temperature along the centreline is Circle, Hexagon,

Inverted Equilateral triangle, Square, Equilateral triangle. The

decreasing order of peak velocity along the centreline is Equilateral

triangle, Inverted Equilateral triangle, Circle, Square, Hexagon.

Temperature regainment distance is maximum for Equilateral triangle

and the decreasing order is Equilateral triangle, Hexagon, Inverted

Equilateral triangle, Square, Circle. Velocity recirculation distance is

maximum for Square and the decreasing order is Square, Hexagon,

Circle, Inverted Equilateral triangle, Equilateral triangle. In

applications where heat transfer is necessary, Circular cross section

can be implemented and in applications where heat transfer is to be

minimum, Equilateral triangle can be implemented as it has the

maximum temperature regainment distance.

Page | 34

References

[1] H. HU AND M. M. KOOCHESFAHANI 2011, Thermal effects on the wake of heated cylinder operating in a mixed

convection regime, Cambridge University Press

[2] Y BAO, J TAO 2013, The passive control of wake flow behind a circular cylinder by parallel dual plates, Journal of

fluids and structures

[3] A DALOGLU, A UNAL 2000, Heat transfer from a cylinder in the wake flow

[4] C.W.WONG , Y.ZHOU, MD.MAHBUB ALAM , T.M.ZHOU , 2014, Dependence of flow classification on

Reynolds number for a two-cylinder wake, Journal of fluids and

structures

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