Çukurova university institute of natural and applied ... · türbülanslı akışta orifis...

ÇUKUROVA UNIVERSITY

INSTITUTE OF NATURAL AND APPLIED SCIENCES

MSc. THESIS

Mustafa OĞUDAY

FLOW CHARACTERISTICS AROUND ORIFICE USING PIV TECHNIQUE

DEPARTMENT OF MECHANICAL ENGINEERING

ADANA, 2010

Not: The usage of the presented specific declarations, tables, figures, and photographs either in thesis or in any other reference without citiation is subject to “ The Law of Arts and Intellectual Products” numbered 5846 of Turkish Republic.

INSTITUTE OF NATURAL AND APPLIED SCIENCES

UNIVERSITY OF CUKUROVA


By Mustafa OĞUDAY

M.Sc. THESIS

DEPARTMENT OF MECHANICAL ENGINEERING

We certified that the thesis titled above was reviewed and approved for the award of

degree of Master of Science by the board of jury on ……………..

Signature

Signature

Signature

Assoc. Prof.Dr. Hüseyin AKILLI Assoc. Prof.Dr. Ahmet PINARBAŞI Assist. Prof.Dr.Sami AKÖZ

Supervisor Member Member

This M.sc. Thesis is performed in Department of Mechanical Engineering of Institute

of Natural and Applied Sciences of Cukurova University.

Registration Number:

Prof. Dr. İlhami YEĞİNGİL

Director

The Institute of Natural and Applied Sciences

I

ABSTRACT

M.Sc. THESIS


Mustafa OĞUDAY

DEPARTMENT OF MECHANICAL ENGINEERING INSTITUTE OF NATURAL AND APPLIED SCIENCES

UNIVERSITY OF ÇUKUROVA

Advisor : Assoc. Prof. Dr. Hüseyin AKILLI Year: 2010, Pages: 55

Jury : Assoc. Prof. Dr. Hüseyin AKILLI

: Assoc. Prof. Dr. Ahmet PINARBAŞI : Assist. Prof. Dr. Sami AKÖZ

The main purpose of the present study is to investigate the details of flow structure downstream of an orifice plate with variable thickness inserted in a pipe in turbulent flows using Particle Image Velocimetry (PIV) technique for Reynolds numbers based on the pipe diameter ranging from 7 400 to 37 000. The ratio of orifice diameter to the pipe diameter, β=0.6, was kept constant, but dimensionless orifice plate thickness ratio t* was varied from 1/8 to 1 throughout for turbulent flows. The flow data downstream of the orifice plate in consecutive side-view planes are presented using time-averaged velocity vector map, streamline patterns, vorticity contours. Variation of time-averaged velocity vectors along a specific line is also presented graphically.

Keywords: Orifice meter, turbulent flow, the PIV technique.

II

ÖZ

YÜKSEK LİSANS TEZİ

PIV TEKNİĞİ KULLANILAN ORİFİS ETRAFINDAKİ AKIŞ

KARAKTERİSTİĞİ

Mustafa OĞUDAY

ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ

MAKİNA MÜHENDİSLİĞİ ANABİLİM DALI

Danışman : Doç. Dr. Hüseyin AKILLI Yıl: 2010, Sayfa: 55

Jüri : Doç. Dr. Hüseyin AKILLI

: Doç. Dr. Ahmet PINARBAŞI : Yrd. Doç. Dr. Sami AKÖZ

Mevcut çalışmanın başlıca amacı; Reynolds sayısı 7 400 ile 37 000 arasında değişen türbülanslı akışta, boru içerisine yerleştirilmiş değişik et kalınlıklarındaki orifisin çıkıştaki akış yapısı detaylarının türbülanslı akış ortamında PIV tekniği kullanarak incelemektir. Türbülanslı akışta orifis çapının boru çapına oranı olan β sabit olarak 0.6’ya eşit tutulup orifis kalınlık oranı t* ise 1/8 ile 1 oranları arasında değişmektedir. Orifisin çıkışındaki akış bilgileri yan görünüş düzlemlerindeki ortalama girdap eğrileri, akım çizgileri ve vektör haritaları kullanarak sunulmuştur. Ayrıca, ortalama hız vektörlerinin belirli bir çizgi boyunca değişimi grafiksel olarak sunulmuştur.

Anahtar Kelimeler: Orifis metre, türbülanslı akış, PIV.

III

TEŞEKKÜR

Yapılan çalışmaların her aşamasında, desteğini ve yakın ilgisini benden

esirgemeyen değerli hocam Doç. Dr. Hüseyin AKILLI’ya en derin saygılarımı ve

minnettarlığımı ifade etmek isterim.

Deneylerin yapımında ki yardımlardan dolayı ve çalışmanın her aşamasında

bilgilerinden yararlandığım Dr. Sedat Yayla’ya ve Proje Asist. Engin Pınar’a

teşekkür ederim.

Bu çalışma süresi boyunca benden manevi desteğini esirgemeyen sevgili eşim

Elif Oğuday’ a sonsuz teşekkür ederim.

Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Makine Mühendisliği

Bölümünde eğitim gördüğüm süre içerisinde beraber çalıştığım tüm akademik ve

idari görevlilere ayrıca teşekkür ediyorum.

Bu çalışmanın ülkeme faydalı olmasını diliyorum.

IV

TABLE OF CONTENTS PAGE

ABSTRACT.................................................................................................................. I

ÖZ.................................................................................................................................. II

ACKNOWLEDGEMENT……………………………………………………………. III

TABLE OF CONTENTS ………………………………………………………...….. IV

LIST OF FIGURES ……………………………………………………………......... V

NOMENCLATURE………………………………………………………………….. VII

1. INTRODUCTION…………………………………………………………………. 1

1.1. Flow Separation………………………………………………………………. 5

1.1.2. Streamline Characteristics at the Wall………………………………..... 5

2. LITERATURE SURVEY………………………………………………………….. 7

3. MATERIAL AND METHOD……………………………………………………... 12

3.1. Experimental Set-Up.…….…………………………………………………... 12

3.2. Measurement Technique……………………………………………………… 13

3.2.1. Particle Image Velocimetry Technique………………………………... 13

3.2.1.1. Principles of PIV……………………………………………..... 15

3.2.1.2. Seeding……………………………………...……………….... 16

3.2.1.3. Illumination……..……………………………………………... 17

3.2.1.4. Cameras (Image Capturing)………………………………….... 18

3.2.1.5. Correlation (Image Evaluation)……………………………….. 18

3.2.1.6. Validation and further analysis (Image Post-Processing)……... 20

3.2.1.7. Time-Averaging of PIV Images……………………………..... 21

4. RESULTS AND DISCUSSIONS............................................................................. 23

5. CONCLUSIONS………………………………………………………………….. 50

REFERENCES……………………………………………………………………….. 52

CURRICULUM VITAE……………………………………………………………… 55

V

LIST OF FIGURES PAGE Figure 1.1. Schematic demonstration of pipe flow ………………………………… 1

Figure 1.2. Configuration of orifice plate…………………………………………... 3

Figure 1.3. 3-D skin friction lines………………………………………………….. 6

Figure 3.1. Schematic representation of experimental set-up…………………….... 13

Figure 3.2. Schematic arrangement of the PIV system…………………………….. 14

Figure 3.3. PIV overview (Schiwietz, T., Westermann, R., 2004)…………………. 19

Figure 4.1. Schematic drawing of the experimental measuring test section……….. 24

Figure 4.2. Time-averaged velocity map,<V> streamline patterns, <ψ> and

vorticity contours, <ω> in side-view plane Red = 7400 and t* are ;

a)1/8 b)1/4 and c)1 , minimum and incremental values of vorticity are

ωmin =±150s-1 and ∆ω =10s-1.................................................................... 25


vorticity contours, <ω> in side-view plane Red = 14 800 and t* are; a)

1/8 b) 1/4 and c)1 , minimum and incremental values of vorticity are

ωmin =±300s-1 and ∆ω =10s-1……………………………………………

26




ωmin =±400s-1 and ∆ω =20s-1…………………………………………… 27




ωmin =±400s-1 and ∆ω =20s-1…………………………………………… 28




ωmin =±600s-1 and ∆ω =20s-1…………………………………………… 29

VI

Figure 4.7. The demonstration of different t* values on flow at Red=7 400 ………. 31

Figure 4.8a. The demonstration of vena contracta at different t* values for

Red=7400……………………………………………………………….. 33

Figure 4.8b. The demonstration of vena contracta at different Reynolds numbers for

t*=1/8…………………………………………………………………... 34

Figure 4.9. The demonstration of velocity jet at different t* values for Red=14800.. 37

Figure 4.10a. Graphics for relationship between u (mm/s) and y (mm) spanwise

distance at Red=7 400……………………………….............................. 39

Figure 4.10b. Graphics for relationship between u (mm/s) and y (mm) spanwise

distance at Red=7 400…………………………………………………... 40

Figure 4.11a. Graphics for relationship between Reynolds stress (u’v’) and y (mm)

spanwise distance at Red=7 400………………………………………... 42

Figure 4.11b. Graphics for relationship between Reynolds stress (u’v’) and y (mm)

spanwise distance at Red=7 400………………………………………... 43

Figure 4.12a. Graphics for relationship between urms (mm/s) and y (mm) spanwise

distance at Red=7400…………………………………………………… 44

Figure 4.12b. Graphics for relationship between urms (mm/s) and y (mm) spanwise

distance at Red=7 400…………………………………………………... 45

Figure 4.13a. Graphics for relationship between u, u’v’ and urms and y (mm)

spanwise distance at Red=7400 and different x distances for t*=0.125... 46

Figure 4.13b. Graphics for relationship between u, u’v’ and urms and y (mm)

spanwise distance at Red=7400 and different x distances for t*=0.25…. 47

Figure 4.13c. Graphics for relationship between u, u’v’ and urms and y (mm)

spanwise distance at Red=7400 and different x distances for t*=1…….. 48

VII

NOMENCLATURE A : Cross-sectional area of the pipe, m²

C : Orifice flow coefficient, dimensionless

Cd : Orifice discharge coefficient, dimensionless

do : Diameter of the orifice (m)

D : Diameter of the pipe (m)

f : Friction factor

L : Pipe length (m)

P : Pressure (Pa)

Q : Volumetric flow rate (m3/s)

t* : Ratio of the orifice’s thickness to the orifice’s diameter

t : Time (s)

Reo : Reynolds number based on orifice’s diameter

Red : Reynolds number based on pipe’s diameter

Sx : Saddle point

Fx : Focus

Na : Nodal point of attachment

Ns : Nodal point of separation

<V> : Time-averaged velocity

V : Instantaneous velocity

<ψ> : Time-averaged streamline

ψ : Instantaneous streamline

<ω> : Time-averaged vorticity

ω : Instantaneous vorticity

u’,v’ : Fluctuating velocity components (mm/s)

∆t : Time interval

β : Ratio of the orifice’s diameter to the pipe’s diameter

µ : Dynamic viscosity (kg/ms)

ρ : Density (kg/m3)

1. INTRODUCTION Mustafa OĞUDAY

1

1. INTRODUCTION

Flow rate measurement is very important in the most of industry process, and

its important has increased in the last 50 years. In other words, it was widespread use

for accounting purposes, such as custody transfer of fluid from supplier to customers,

includes food and beverage, oil and gas industrial, medical, petrochemical, power

generation, and water distribution and etc.

Also, measurement of flow is a critical need in many industrial plants. In

some operations, the ability to conduct accurate flow measurements is so important

that it can make the difference between making a profit or taking a loss. Furthermore,

inaccurate flow measurements or failure to take measurements can cause serious

results.

Flow measurement is the determination of the quantity of a fluid, either a

liquid, or vapour, that passes through a pipe, duct or open channel. Flow may be

expressed as a rate of volumetric flow, mass rate of flow, or in terms of a total

volume or mass flow.

There are different types of measuring the flow rate of fluid flowing in a pipe.

One of the most greatly used flow meters in the industry is based on the

measurement of the pressure difference created when forcing the fluid flow through a

constriction in the pipe as shown in Figure 1.1.

Figure 1.1. Schematic demonstration of pipe flow

Flow direction

point of max velocity min pressure 2 1


2

The relationship between flow rate and pressure difference is determined by

the Bernoulli equation, assuming that changes in elevation, work and heat transfer

are negligible, shortly Bernoulli's principle which says that there is a relationship

between the pressure of the fluid and the velocity of the fluid. When the velocity

increases, the pressure decreases and vice versa.

Also assuming flow is steady-state, incompressible, inviscid, laminar flow in

a horizontal pipe with negligible frictional losses, Bernoulli's equation reduces to an

equation relating the conservation of energy between two points on the same

streamline:

Bernoulli's equation:

By continuity equation:

Solving for Q:

The above expression for Q gives the theoretical volume flow rate.

Introducing the beta factor β= d2 / d1 as well as the coefficient of discharge Cd:

The most commonly used device for metering flows is the orifice meter,

which is a geometrically simple device. An orifice plate is a plate with a hole in the


3

middle. It is usually placed in a pipe in which fluid flows. The typical orifice plate

has a concentric, sharp edged opening, as shown in Figure 1.2. It restricts the flow

and measuring the pressure differential across the constriction gives the flow rate.

Figure 1.2. Configuration of orifice plate

The discharge coefficient (Cd) for orifice meters is normally obtained using

empirical equations as indicated before. These are obtained from the experimental

data and derived in check laboratory conditions with having fully developed flow

upstream of the orifice meter. In the case of changing conditions affects the

characteristics of the flow field, and thus alter the discharge coefficients.

Computational fluid dynamics (CFD) models have been used in recent years to

provide initial background for experimental studies to develop experimental

performance (Erdal and Anderson, 1997).

The most critical point in the design of orifice meter is the information of

discharge coefficient related to orifice meter. And to gain this, the flow

characteristics around the orifice meter have been known properly. Flow

characteristics for the orifice can commonly be determined by Navier-Stokes

equations.


4

The solutions of these equations that can not be solved with analytical

methods can be achieved with numerical methods by the help of computers. In this

subject, the critical point is the numerical solution of Navier-Stokes and continuity

equations in laminar and turbulent flows for different flow geometries. There is

demand of solving these types of equations numerically since of the non-linearity of

them. Numerical methods have been improved rapidly as a result of development in

computer technology.

In the present experimental study, the flow characteristics have been

investigated using Particle Image Velocimetry (PIV) technique for orifice plate

which inserted in a pipe and here orifice/pipe diameter ratio β, which is 0.6 and

orifice thickness/diameter ratio t* was changed the range from 1/8 to 1.

The aim of this study was to investigate the effects of orifice plate thickness

and Reynolds number on the flow characteristics using Particle Image Velocimetry

(PIV) technique for turbulent flows. Here, the Reynolds number based on the pipe

diameter ranging from 7 400 to 37 000.

It is well known that the PIV technique can give quantitative information on

the instantaneous spatial structure of the velocity field. Nowadays particle image

velocimetry technique gives an opportunity to the researcher to measure

instantaneous velocity distributions across a defined flow field quantitatively. In

order to demonstrate the characteristics of the flow through the orifice plate, the

formation and development of flow in side view plane downstream of the orifice

plate, 350 images of instantaneous velocity fields were taken. Therefore, in order to

better understand the flow behaviour in the downstream regions of the orifice plate,

the PIV technique is applied to obtain time- averaged flow data in the side-view laser

planes.

The flow data downstream of the orifice plate in consecutive side-view planes

are presented using time-averaged velocity vector map, streamline patterns, vorticity

contours. In addition, variation of time-averaged velocity vectors along a specific

line is also presented graphically.


5

1.1. Flow Separation

The fluid viscosity reduces the fluid particles velocities near to the solid

surface and takes shapes a thin fluid layer called a boundary layer. The flow velocity

is zero at the surface because of the no-slip boundary condition. There is a big

viscous flow resistance in the boundary layer, for that matter the flow momentum is

low. Therefore the boundary layer flow is affected by the pressure gradient. When

the pressure decreases through the direction of the flow, the pressure gradient is said

to be favourable. At the same time, if the pressure increases through the direction of

the flow, an adverse pressure gradient increases as well. In addition, the existence of

a big viscous force, the fluid particles have to move against the increasing pressure

force. As a result of this, the fluid particles could be stopped or reversed, causing the

neighbouring particles to move away from the surface. This phenomenon is called

the boundary layer separation.

1.1.2. Streamline Characteristics at the Wall

At a solid wall skin friction lines can be grouped into these categories

[Filippone, (1999-2004)] into converge to a point, diverge from a point, spiral around

a point, deviate from a point, converge to a line, diverge from a line. If the skin

friction lines converge to or diverge from a point, the point is called Node. Nodal

points can have one line to which all skin friction lines are tangent to, or none. Nodal

points of separation and attachment can be showed as sinks and sources of skin

friction, respectively. There are situations where the skin friction lines deviate from a

point as from a stagnation point. And, there are only two lines to the point, which is

called Saddle. One of the lines through the saddle is a separation line. Nodal points

of separation and attachment are other important characteristics: they become edges

of vortex cores. These properties and definitions can be seen as below Figure 1.3.


6

Figure 1.3. 3-D skin friction lines

2. LITERATURE SURVEY Mustafa OĞUDAY

7

2. LITERATURE SURVEY

A great number of investigations on the pipe orifice flows have been done so

far. An experimental study of Johansen (1930), has been on the flow discharge

coefficient of water through a sharp-edged circular orifice for 0Re values in the

range 40 107.5Re0 ×≤< with the orifice/pipe diameter ratio β varying from 0.2 to

0.8 for a constant orifice thickness/diameter ratio t*. Here, 0Re is based on the orifice

diameter.

Mills (1968), have obtained numerical solutions of Navier-Stokes equations

for Reo values in the range 0 ≤ Reo ≤ 50 which steady, axisymmetric, viscous,

incompressible fluid flow with a fixed orifice/pipe diameter ratio of β=0.5 and a

fixed orifice thickness/diameter ratio t*, by means of the predictions have complied

well with the experimental results obtained by Johansen (1930).

A technique for the numerical solution of the unsteady Navier-Stokes

equations for laminar flow through the orifice plate within a pipe has been obtained

by Coder and Buckley (1973). They gained the solution through the rearrangement of

the equations of motion into a vorticity transport equation and a definition-of-

vorticity equation, which are solved by an implicit numerical method.

An extensive experimental study has been done by Alvi et al (1978), on the

loss characteristics and discharge coefficient of the sharp-edged orifices, quadrant-

edged orifices and nozzles for Reynolds numbers, based on pipe diameter, in the

range 20 ≤ Re ≤ 104 with varying β, at the constant orifice thickness/diameter ratio.

A numerical algorithm for the solution of steady flow of a viscous fluid through

a pipe orifice that allows a considerable flexibility in the choice of orifice plate

geometry with a constant thickness has been investigated by Nigro et al (1978).

Şahin et al (1988), have studied the flow characteristics through the orifice

plate between orifice thickness ratios 0.078 < t* < 1 and they have obtained that as

the orifice thickness changes discharge coefficient of orifice also changes.

A new numerical method for treating the vorticity singularity of

incompressible viscous flow around a re-entrant sharp corner has been used by Ma


8

and Ruth (1992). They have improved vorticity circulation method for contracting

flow, which was characterized by the local flow acceleration and separation, based

on comparisons of the ad hoc methods and the Moffat expansion method.

Morrison et al (1995), have studied the response of the orifice meter to get

upstream flow field disturbances generated by a concentric flow conditioner and a

vane-type swirl generator. They have investigated two different flow rates with eight

orifice plates with β ratios of 0.43, 0.45, 0.48, 0.55, 0.6, 0.65, 0.7 and 0.73. The

response of each orifice meter to the disturbance was characterized by measuring the

axial wall pressure distribution near the orifice plate and the discharge coefficient.

Şahin and Ceyhan (1996), have examined the flow characteristics through the

square-edged orifice inserted in a pipe both numerically and experimentally. They

have solved the governing equations assuming that flow was steady, fully developed,

laminar, incompressible, two-dimensional and axisymmetric with Reynolds numbers

in the range 0 ≤ Reo ≤ 144 and the orifice thickness/diameter ratio in the range

1/16 ≤ t* ≤ 1. They have observed that length of separated flow region changes rapidly

especially at low Reynolds numbers.

Şahin and Akıllı (1997), have studied a numerical analysis of laminar flow

through square-edged orifice for Reynolds numbers in the range of 0 ≤ Reo ≤ 2000

with β values varying from 0.2 to 0.8 and with t* values varying from 1/16 to 1.

They have showed that the flow discharge coefficient gradually decreased when the

orifice thickness/diameter ratio increased for a high porosity.

Erdal and Andersson (1997), have started their studies with a full pipe

simulation to investigate the various grid effects, coordinate arrangements, wall

boundary conditions, differencing schemes and turbulence models that can predict

more accurate flow values through an orifice plate. The calculations were performed

in two-dimensional axisymmetric flow.

Krassow et al (1998), have used a smart-orifice mini head meter which

represents a single compact and economic device for general flow meter

applications. The performance of the mini head meter in water flow measurement

was determined in a computer supported test bench facility. It was compared to the

results predicted by the simulation, as well as to a conventional head meter


9

arrangement with externally mounted pressure transducer, including measurements

with water at elevated temperature and different absolute line pressures. The results

are very promising and verify the competitiveness of the smart-orifice as a mini head

meter.

A finite volume software have been used by Cao et al (2000), to visualize the

flow pattern in a rectangular membrane channel containing net-like materials, which

are the most common spacer or turbulence promoters for membrane processes. They

obtained that both high shear stress regions and eddies are present in the channel due

to the spacer cylinders.

Morrison et al (2001), have studied the effects of adding liquid to a gas flow

upon the metering performances by using a slotted orifice flow meter with an

equivalent β ratio of 0.5 to a two phase flow consisting of air and water.

Borutzky et al (2002), have used an orifice flow model for laminar and

turbulent conditions. Their study have been started from an approximation of the

measured characteristic of the discharge coefficient versus the square root of the

Reynolds number and proposes a single empirical flow formula that provides a linear

relation for small pressure differences and the conventional square root law for

turbulent conditions. Simulation results have proved to be accurate. The orifice

model was easily implemented as a library model in a modern modeling language. In

conclusion, the model could be adapted to approximate pipe flow losses as well.

Sondh et al (2002), have studied the design and development of variable area

orifice meter. Experiments have been performed at different positions of the

symmetrical bodies to evaluate the performance of the variable area orifice meter.

The experiments have shown that a frustum of cone having a hemispherical base and

a parabolic apex gives nearly linear variation of the flow rate with the position of the

body inside the orifice meter and can be adopted for the construction of a variable

area orifice meter.

Singh et al (2003), have developed a methodology for designing a variable

area orifice-meter which the flowrate is indicated by the linear displacement of a

conical body placed symmetrically inside the orifice. The flow field was also

modeled numerically using a commercial computational fluid dynamics (CFD) code


10

‘FLUENT’ and the magnitude of drag force on the body for different positions

relative to the orifice has been calculated. They have observed that as blockage

increases large drag force acts on the body due to form drag and hence, the

differential pressure also increases.

Tu et al (2005), have examined the R134a which was flowing through micro-

orifices with diameters of 31.0 and 52.0 µm, and length-to-diameter ratio of 2.5 and

4.2, respectively. For liquid-upstream/liquid-downstream flow, the discharge

coefficient was found to be independent of Reynolds number, which suggests

separated flow that was defined in macro-scale orifices. The experimental results

indicate significant departure of flow characteristics from macro-scale orifices.

The instantaneous flow characteristics of circular orifice synthetic jet was

experimentally studied using a phase-locked Particle Image Velocimetry (PIV)

system by Xu et al (2006). The aim of their PIV experiment was mainly focused on

the time evolution of the vortex pairs formed in the push cycle, the saddle point

existing in the suck cycle, the variation of the centerline velocity in the whole cycle

and the cross-stream velocity profiles and their self-similarity. Also, they have

changed the depth of orifice from 1.5 mm to 2 mm and 3.5 mm in order to study the

effect of different orifice depths on the flow structure, which shows that at all stream

wise sections, the peak of the mass flux and momentum flux increases as the orifice

depth increases.

Ahn et al (2007), have investigated the characteristics of continuous, steady

granular flow through a flat-plate orifice. Discharge rates of granular particles

through the orifice have been studied as a function of the average normal stress on

the orifice plate. The results showed that granular flows through the orifice are

characterized by three regimes. When the flow was not choked, the discharge rate

has increased with the increasing normal stress (Regime I).With the further increase

of the normal stress, the discharge rate has reached a maximum, at which the flow

appears to start choking. Once the flow has become choked, the discharge rate has

started decreasing (Regime II) for further increase of the normal stress and then has

become independent of the normal stress on the orifice plate (Regime III).

Aly et al (2009), have investigated the pressure drop after fractal-shaped


11

orifices, which have a significant effect on the flow mixing properties downstream a

pipe owing to their edge self-similarity shape, and measured the pressure recovery at

different stations downstream the orifice. Their results showed that the fractal-shaped

orifices have a significant effect on the pressure drop. Furthermore, the pressure drop

have measured across the fractal-shaped orifices was found to be lower than that

from regular circular orifices of the same flow areas. This result could be important

in designing piping systems from the point of view of losses.

3. MATERIAL and METHOD Mustafa OĞUDAY

12

3. MATERIAL and METHOD

3.1. Experimental Set-Up

A schematic view of experimental set-up is presented in Figure 3.1. The

experiment is performed in Çukurova University, Fluid Mechanic Laboratory of

Mechanical Engineering Department, Turkey.

There is a mica pipe has the following dimensions; a length of 2000mm, wall

thickness of 3mm and a diameter of 60 mm. This first pipe is used to eliminate the

bubles than, a second pipe has same properties with first one is used as seen in Figure

3.1. This second pipe has an orifice inserted in it. Also, an aquarium is used to avoid

the refraction of laser beam. Second pipe is inserted into that aquarium. As shown in

schematic representation of experimental set-up, two water tanks having 0,2m3

volume, one water pump, one flowmeter and one filter are used to complete the

experiment closed cycle.

Water comes from first water tank which is approximately mounted 6 meter

height from experiment set-up, and the water flows over respectively filter,

flowmeter, first pipe and second pipe. While the flow passes from second pipe and

orifice plate, the images are taken by camera helping with laser beams.

The images were taken just behind of orifice plate. Finally, the water

discharges to second water tank and pumps through the upper tank by water pump.

So, the closed cycle is completed.

In order to characterize the flow structure downstream of the orifice plate, a

technique of high-image-density particle image velocimetry (PIV) is employed.


13

Figure 3.1. Schematic representation of experimental set-up

3.2. Measurement Technique

3.2.1. Particle Image Velocimetry Technique

The Particle Image Velocimetry (PIV) technique, which allows

instantaneous, non-intrusive and quantitative measurement of two dimensional flow

field is an important achievement and a well established technique in many areas of

modern experimental fluid mechanic applications. PIV also provides sufficient

spatial resolution such that an instantaneous vorticity field may also be calculated.

PIV has been used to measure velocity vector fields from slow flows to supersonic

flows during past two decades (Adrian, 1991; Raffel and Kompenhans, 1995; Raffel,

et al, 1998).The technique involves seeding the flow field, illuminating the region

under investigation and capturing two images of that region in rapid succession.

From the displacement of the tracer particles, provided that the time interval between

image captures is known, a velocity vector map can be calculated in the flow field.


14

The theory of PIV was introduced by Adrian (1988) in the late 1980s with

the first experimental implementations following shortly afterwards (Kean et al. 1990

and Kean et al. 1991). At the stage, due to hardware limitations, a single

photographic frame was multiply exposed and analysed using an auto-correlation

technique. However, improved speed of photographic recording soon allowed images

to be captured on separate frames for analysis by cross-correlation (Kean et al. 1992).

Figure 3.2. Schematic arrangement of the PIV system

Also, Figure 3.2 briefly explains a typical set up for PIV recording. Small

tracer particles are added to the flow. A plane (light sheet) within the flow is

illuminated twice by means of a laser (the time delay between pulses depending on

the mean flow velocity and the magnification at imaging). It is assumed that the

tracer particles move with local velocity between the two illuminations. The recorded

via a high quality lens either on a single photographical negative or on two separate


15

frames on a special cross correlation CCD camera. After development the

photographical PIV recording is digitized by means of a scanner. The output of the

CDD camera is stored in real time in the memory of a computer directly. As the

resolution and image format of CDD camera is several orders of magnitude lower

than that of a photographic medium, digitization cannot be ignored.

3.2.1.1. Principles of PIV

Particle Image Velocimetry (PIV) is a measurement technique based on the

basic equation as shown below.

For the PIV technique the property actually measured is the distance

between two images of particles that travels in the flow field within a known time

interval. These particles are added to the flow and known as seeding. The type of

seeding particle is chosen to follow the flow, and in order to detect their movement,

an area of the flow field is illuminated by a laser light-sheet. The light-sheet, which is

generated by a laser and a system of optical components, is not

continuous/permanent, but pulsed to produce a stroboscopic effect, freezing the

movement of the seeding particles. The time between the light pulses is the

denominator in the equation above. To detect the position of the illuminated seeding

particles, a CCD-camera (CCD = Charge Coupled Device) is positioned at right

angles to the laser light-sheet, and particle positions will appear as light specks on a

dark background on each camera frame. The pulsing light-sheet and the camera are

synchronized so that particle positions at the instant of light pulse number 1 are

registered on frame 1 of the camera, and particle positions from pulse number 2 are

on frame 2. (Older generations of CCD cameras couldn’t switch frames fast enough,

so both the first and the second pulse of the light sheet was recorded on the same

camera frame).

Speed (V) = Distance (x) / Time (t)


16

The camera images are divided into square regions called interrogation areas

or interrogation regions, and for each of these interrogation areas the image from the

first and the second pulse of the light-sheet are correlated to produce an average

particle displacement vector. Doing the same process for all interrogation regions

produce a vector map of average particle displacements. Dividing with the known

time between the two images captured the displacement vectors are converted into a

map of so-called raw velocity vectors. Then validation algorithms can be applied to

the raw vector maps, so that outliers, the term for erroneous vectors, can be detected

and removed. In the FlowMap PIV system, for reasons of experimental

reproducibility, the raw vector map is archived and a new validated vector map is

output, and further analysis can produce streamlines, vorticity and so on.

From the basic principles the following main topics of PIV emerge:

• Seeding

• Illumination

• Cameras

• Synchronization

• Correlation

• Validation and further analysis

3.2.1.2. Seeding In a few case it is possible to make sure measurement using what is

naturally present as impurities in the fluid, but usually, successful seeding can

require considerable effort and ingenuity.

There are some factors that have to be considered such as flow medium

(air/water), volume to be seeded, light scattering, flow velocity, particle image size,

safety considerations (risk of explosion, ingestion) and cost.

Particle size and density, and fluid density and viscosity determine the

effects of buoyancy and inertia. Exact neutral buoyancy is difficult to achieve, but

particles must remain suspended throughout an experiment.

The light scattered from the particles is only a fractions of the light

introduced into the flow. This scattered light only that within the solid angle defined


17

by the lens aperture of the imaging system will be collected to form an image.

Conventional PIV set-ups record side-scattered light, which can be orders of

magnitude weaker than forward-scattered light. The size and material of the seed

particles can affect scattering efficiency and small particles also affect particle image

intensity. The average particle image should exceed the fog level of photographic

emulsions or the noise level of solid-state detectors.

3.2.1.3. Illumination

The displacement field is determined as average displacements within so-

called interrogation areas of the image plane in PIV technique. A typical size of these

interrogation windows is 32x32 pixels, which means that a gets about 7300 vectors

from an image with a resolution of 1600×1186 pixels. For single exposed images, the

displacement is determined by forming an adaptive cross-correlation of

corresponding interrogation areas in the first and second images. The location of the

highest correlation peak in the correlation plane corresponds to the most likely

average particle displacement in the interrogation area. Sub-pixel accuracy of the

displacement is obtained by fitting a Gaussian distribution to the correlation peak,

and finding the exact peak location. Since the cross-correlation method uses all

information within the interrogation area for finding the displacement, the method is

robust and often provides reasonable results even for non-ideal conditions. Another

advantage is that the displacement field is obtained on a regular grid.

For the illumination, it is preferable to use a laser, since the laser beam is

easy to form into a sheet by a cylindrical lens. A pulsed laser is to prefer, since one

obtains a high light energy during a very short time interval (typically 5 ns for a

YAG-laser), which means that the particle images will be practically frozen even for

high velocities (> 100 m/s). The repetition rate of a YAG-laser is typically 10-30 Hz,

which is too low except for very low velocities (< 1 cm/s). One therefore needs two

lasers to get full freedom in terms of time separation between the pulses. Special PIV

YAG-lasers are available that combine two laser cavities with a common beam

outlet.


18

3.2.1.4. Cameras (Image Capturing)

To be able to acquire two single exposed images with a time separation of

the order of microseconds, one uses a so-called full-frame interline transfer

progressive scan CCD camera, also called a cross-correlation CCD-camera. The

basic idea is that the image exposed by the first laser pulse is transferred very rapidly

to light-hidden areas on the CCD-chip. This is done on a pixel-by-pixel basis, i.e.

each pixel has its own storage site in immediate vicinity of the light sensitive pixel

area. After the second exposure, both images are transferred to the computer. Since a

lot of data has to be transferred, it is only possible to take a few double-images per

second. The temporal resolution of the flow is thus in general very poor with this

technique.

A very important issue for obtaining accurate PIV measurements is the

appropriate seeding of the flow with tracer particles. To closely follow the flow the

particles should be as small as possible, but on the other hand they may not be too

small, because then very small particles will not scatter enough light, and hence

produce too weak images.

3.2.1.5. Correlation (Image Evaluation)

Since the introduction of the first PIV image evaluation methods, alternative

analysis algorithms have been developed as well as error correction and post-

processing procedures designed to improve speed and accuracy of the PIV method.

However, the classical PIV analysis method is still the most frequently used and

forms the basis of many other algorithms. (Figure 3.3.).


19

Figure 3.3. PIV overview (Schiwietz, T., Westermann, R., 2004)

The heart of the PIV analysis is the correlation of regions of the input

images (known as interrogation areas) with each other to determine the displacement

vector of the flow in that part. Knowing the time interval between the image captures

enables a velocity vector to be calculated from the displacement vector. The

correlation technique can be used for a single frame multiple exposed (auto-

correlation) or multiple frames singly exposed (cross-correlation). To speed up the

convolution process, correlation of each pair of interrogation areas is carried out in

Fourier space. After interrogating the images in this way and generating the vector

map, post-processing is carried out to validate the data and to improve the vector

map resolution and accuracy. Using this vector map, vorticity and Reynolds stress

contours and streamline topology can be obtained.


20

3.2.1.6. Validation and further analysis (Image Post-Processing )

Images were received from CCD camera that has resolution 1,600 ×11.186

pixel at a rate of 15 frames per second. The time delay changes from 1.7 ms and 4.5

ms between frames depending on the flow conditions and camera location. Digital

image was analyzed using FLOWMAP software. The image was recorded on a CDD

array. A frame grabber in the computer read the camera image from CCD camera

and stored it as the digital image file format (TIFF) in the RAM. This digital image

was processed and analyzed using the FLOWMAP software. During each continuous

run, a total 390 images were taken. In order to determine the velocity field, a

cross-correlation technique, with 32×32-interrogation window, was employed, with

an overlap of % 50.

The resulting vector field obtained from FLOWMAP software and the

corresponding boundaries of objects were then viewed using program V3 to

determine incorrect vectors from interrogation. These types of vectors can result

when an incorrect particle correlation is made near boundaries or within shadow

regions, when the particle images are too widely spaced for interrogation window

side specified, pr the power of laser sheet is poor.

Vector validation software called CLEANVEC was used to remove

incorrect vectors.

The software CLEANVEC contains four statistical filters designed for

incorrect vectors removal:

• Absolute range filter

• RMS tolerance filter

• Magnitude difference filter

• Quality filter

Three of these four filters were used for the purposes of eliminating incorrect

vectors. Here the quality filter requires a correlated data, which are supposed to be

done by interrogation and this data, was not provided by this software.

In the absolute range filter, all streamwise and spanwise velocity components

that lie outside of given range were removed. With this filtering method, one can


21

identify a moving reference frame in order to save real vectors that are numerically

specified and eliminated incorrect vectors on the main frame. Although very trivial,

this filter might be very useful in removing the most tedious incorrect vectors, and

hence improves the performance of the other filtering tools.

The RMS tolerance filter removes incorrect vectors those lay outside of

given range. This filter must be applied to a velocity field in a reference frame

moving with the mean velocity components in both directions, since it is involved

with the fluctuating components only.

Also, the magnitude difference tool removes unnecessary vectors based on

the difference in magnitude between a vector and its neighborhood median. This is

the local-median test defined by Westerweel (1994). This filter is the most effective

among the available filters, as indicate by Westerweel (1994). However, it should be

handled carefully, because it may lead to an excessive vector in a certain type of

flows.

Finally, the vorticity was calculated by circulation method. The velocity and

vorticity data were set to zero in the region containing the bluff body following the

smoothing process and vorticity calculation. The contours of constant vorticity were

constructed using a spline fit technique with a tension factor of 0.1 for smoothing

process.

3.2.1.7. Time-Averaging of PIV Images

Time-averaging of PIV images were performed using following

formulation. Time-averaged horizontal component of velocity:

( )∑=

=N

1nn y,xu

N1u (3.1)

Time-averaged transverse component of velocity:


22

( )∑=

=N

1nn y,xv

N1v (3.2)

Time-averaged vorticity:

( )∑=

ω=ωN

1nn y,x

N1 (3.3)

Root-mean-square of u component fluctuation:

( )[ ]212N

1nnrms y,x(uy,xu

N1u

−= ∑=

(3.4)

Root-mean-square of v component fluctuation:

( )[ ]212N

1nnrms y,x(vy,xv

N1v

−= ∑=

(3.5)

Averaged value of Reynolds stress correlation:

( )[ ] ( )[ ]y,x(vy,xvy,x(uy,xuN1vu n

N

1nn −−=′′ ∑

=

(3.6)

Where N is the total number of instantaneous images used for the time-

averaged values and n refers to the instantaneous images.

4. RESULTS and DISCUSSION Mustafa OĞUDAY

23

4. RESULTS and DISCUSSION

In the present experimental study, it is aimed to investigate the flow details in

the region downstream of an orifice plate inserted in a pipe flow. In the literature, the

behaviour of flow characteristics through the orifice plate has been investigated

commonly by using numerical methods. It is well known that the PIV technique can

give quantitative information on the instantaneous spatial structure of the velocity

field. Also, the PIV technique is applied to obtain time-averaged flow data in the

side-view laser planes in order to better understand the flow behaviour in the

downstream regions of the orifice plate.

In this study, t* values of the square-edged orifice plate inserted in a pipe

were varied to observe the orifice plate thickness effect. According to the

international standards [ANSI/API 22530], t* should not be greater than 1/8. But in

this study variation of characteristics of flow field with Red in the range

7400 ≤ Red ≤ 37000 for β value of 0.6 and t* values in the range 1/8 ≤ t*≤ 1 were

examined experimentally.

The orifice plate, which was used in this experiment, was manufactured from

teflon using turning machine. Dimensions of the orifice plate were measured by

using electronic caliper gage. The accuracy of that electronic caliper gage is

0,001mm. The orifice plate was inserted into the pipe as close fit.

The images were taken just behind of orifice plate to investigate the

characteristics of downstream flow by using PIV. For tests conducted in side-view

planes, observed flow region is seen in Figure 4.1 as called measuring section.


24

Flow direction

Figure 4.1. Schematic drawing of the experimental measuring test section

Time-averaged velocity vector map, <V>, streamline patterns, <ψ> and

corresponding vorticity contours, <ω> in the downstream of orifice plate in side-

view plane for five different Reynolds numbers 7400, 14800, 22200, 29600 and

37000 at three different thickness ratio, t*, values 1/8, 1/4 and 1, have obtained from

PIV data. The following figures show the thickness ratio, t*, effect on flow

characteristics for each Reynolds number.

Şahin and Ceyhan (1996) have indicated that the separated flow region,

which surrounds the emerging core flow, occupies a wider space while Reynolds

number increases. Also, they have examined that at an orifice plate

thickness/diameter ratio 1/4 ≤ t* ≤ 1, the flow characteristics are formed in the forward

face of the orifice do not show any variation. Boundary of the separated flow region

formed in the flow after the orifice plate is understood by looking at following

figures especially in streamline patterns. General information about the flow can be

obtained from time-averaged velocity vector map, <V>, streamline patterns, <ψ> and

corresponding vorticity contours, <ω>.

Figures 4.2, 4.3, 4.4, 4.5 and 4.6 show time-averaged velocity vector map,

<V>, streamline patterns, < ψ > and corresponding vorticity contours, < ω > in the

downstream of the orifice plate in side-view planes for measuring section and for

five different Reynolds numbers 7400, 14800, 22200, 29600 and 37000. The flow is

in x-direction. These figures are grouped to show the effect of thickness/diameter

ratio, t*, on the flow structure. In the field of time-averaged vorticity contours, <ω >,

Orifice Plate

Pipe

Measuring Section


25

patterns of negative vorticity are indicated with dashed lines, on the other hand,

positive vorticity are indicated with solid lines.

Figure 4.2. Time-averaged velocity map,<V> streamline patterns, <ψ> and vorticity

contours, <ω> in side-view plane Red = 7400 and t* are ; a)1/8 b)1/4 and c)1 , minimum and incremental values of vorticity are ωmin =±150s-1 and ∆ω =10s-1


26


contours, <ω> in side-view plane Red = 14 800 and t* are; a) 1/8 b) 1/4 and c)1 , minimum and incremental values of vorticity are ωmin =±300s-1 and ∆ω =10s-1


27




28




29



From the time-averaged flow data illustrated in Figures 4.2, 4.3, 4.4, 4.5 and

4.6 the behavior of the flow in downstream of orifice plate can be seen clearly, it is

known that when the flow passes from the orifice plate the flow structure changes in

comparison with upstream of flow structure. The flow separation occurs due to

pressure gradient, and vortices start to appear upper and lower part of the pipe. These

vortices are symmetrical and have opposite directions.

In addition to these, in turbulent flow, as the thickness of the orifice plate

increases, the flow separation occurs in the orifice bore. Namely, both detachment

and reattachment of flow occur before flow leaves the orifice plate.


30

The occurrence of the separation at the rear side of the orifice plate causes

further increase in pressure losses. From the previous studies, it can be concluded

that decreasing gradient of the discharge coefficient values in thicker orifice plate is

higher than that occurs in thinner one in turbulent flows.

It is known that the distributions of streamlines indicate that the size of the

separated flow region, which surrounds the jet, is bigger corresponding to the results

of thicker orifice plate for laminar flow by looking at previous studies. Flow is

entrained into the edge of the jet in the mixing region giving rise to a circulatory

motion within the separated flow. It was also seen that the length of separated flow

region continuously decreased in size with increasing the thickness of the orifice

plate t* for laminar flows. On the other hand, the point of reattachment of the jet

moves downstream of the previous one and the thickness of the jet becomes

narrower.

In present study, in order to examine the effect of thickness/diameter ratio, t*,

on the flow structure of orifice plate in related region, time-averaged flow data is

investigated in details for turbulent flows. The next figures show the effects of

thickness/diameter ratio, t*, through the flow structure closely.


31

Figure 4.7. The demonstration of different t* values on flow at Red=7 400

In Figure 4.7, the time-averaged streamline patterns are shown clearly. When

the t * is increased separated flow region that have vortices go away from the orifice

plate in x-direction. Also the shape of that region becomes longer and thinner. The

length of separated flow region increases with increasing the Reynolds number.

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0

t * = 1/8

t * = 1/4

t * = 1


32

From the previous studies, Tunay (2002) has denoted that for Reynolds

numbers of Reo=49, 400, 961 the flow begins to separate away at the inlet edge of

the orifice and flow streamlines tend to converge to form a jet, which contracts to a

minimum cross-sectional area some distance downstream of the orifice until a

minimum cross-section of the flow is reached. Also, as mentioned for small values of

t*, such as t*=1/12, the flow separations start from the edge of the orifice and the

inward radial velocity component causes the jet to continue to contract, developing a

minimum cross-sectional area which is called the vena contracta. As soon as

detachment is developed, the size of the separated flow region increases until the

vena contracta. Starting from the cross-section of the vena contracta the flow jet

expands gradually and reattaches to the pipe wall at a point further downstream. The

sudden change of the static pressure is due to the convergence and divergence of the

flow jet that appears in the effective region of orifice. Occurrence of the vena

contracta downstream of the orifice plate indicates that the flow is fully separated in

the vicinity of the orifice bore.

Figure 4.8a presents the relation between thickness / diameter ratio, t*, and

vena contracta behavior for orifice plate. When the t* value is increased from 1/8 to

1, vena contracta occurs closer to orifice plate, in turbulent flows. However, when

the Reynolds number is increased, the vena contracta occurs further from the orifice

plate. This case can be seen in Figure 4.8b.


33

Figure 4.8a. The demonstration of vena contracta at different t* values for Red=7400

0 10 20 30 40 50 60 70

t * = 1 / 8

t * = 1 / 4

t * = 1


34

Figure 4.8b. The demonstration of vena contracta at different Reynolds numbers for t*=1/8

Red= 7 400

Red= 22 200

Red= 37 000


35

By looking to the Figure 4.8a and 4.8b together and examining physics of

flows at related region, it can be answered that why the vena contracta takes place

close or far to the orifice plate downstream. As it is known that when the velocity

decreases as the fluid leaves the orifice the pressure increases and tends to return to

its original level. All of the pressure losses are not recovered because of friction and

turbulence losses in the stream. The pressure drop across the orifice increases when

the rate of flow increases. When there is no flow there is no differential. The

differential pressure is proportional to the square of the velocity, it therefore follows

that if all other factors remain constant, then the differential is proportional to the

square of the rate of flow. The maximum contraction takes place at a section slightly

on the downstream side of the orifice, where the jet is more or less horizontal.

Furthermore, the thickness / diameter ratio, t*, is increased the vena contracta

occurs close to the orifice plate. Because; when the t* is increased, average velocity

of flow just passing from the orifice is low. This reason can be seen clearly in the

forward part of this study which will give velocity values graphically. While the

velocity is decreased, the jet occurs close to the orifice plate. In addition to these, the

increasing of Reynolds number effects to vena contracta as shown in Figure 4.8b.

Examining the same reason with changing t* values of the orifice plate, while the

Reynolds number is increased, averaged velocity at outlet of the orifice plate

increases, so the vena contracta occurs further from the orifice plate.

Revealing the effects of orifice plate on the characteristics of flow is also

possible in terms of the velocity vectors of the flow field. As is the case in streamline

patterns and vorticity contours, velocity vectors also show the maximum variations

of flow characteristics around the orifice plate. It is known that through the flow field

in which the effects of orifice plate are negligible, directions of velocity vectors are

parallel to the central axis of the pipe from the previous studies. But as the flow

comes through the orifice plate, the directions of velocity vectors start to change.

Separated flow region is developed at the rear side of the orifice plate. In this

separated flow region, flow recirculates occupying a wide range of area.


36

In addition to these, Figure 4.9 presents velocity vectors in detail. By looking

this figure, a new point remarks about the length of velocity jet. It can be said that

while the thickness/ diameter ratio value is increased, the length of velocity jet

increase rapidly. Same case is valid for Reynolds number. Namely, when the

Reynolds number is increased, the length of velocity jet increases as well.


37

Figure 4.9. The demonstration of velocity jet at different t* values for Red=14800

10

20

30

40

50

10

20

30

40

50

0 10 20 30 40 50 60 70

10

20

30

40

50

t * = 1/8

t * = 1/4

t * = 1


38

For the investigation of flow characteristics quantitatively, the flow field was

divided into 54 intervals in the vertical direction. Orifice plate is installed 3250 mm

distance from the pipe inlet. So the flow is assumed fully developed just before the

orifice plate.

In this work, the effect of thickness changing has been investigated for

velocity values obtained from PIV data. Different five Reynolds numbers and three

thicknesses are used for experiments (Red; 7400, 14 800, 22 200, 29 600 and 37 000,

t*; 0.125, 0.25 and 1). The values of u, u’v’ and urms values are taken from PIV data.

The graphics of these velocity values are drawn at specified distances in x direction

and three different thicknesses as shown in below figures. In these figures the

Reynolds number is 7400.

The below Figures 4.10a and 4.10b present graphics which show changing of

u values with thickness/ diameter ratio at specified x distance through y direction. As

seen in these graphics for same thickness of orifice plate, while going through the x

direction, the u value is decreasing naturally.


39

Figure 4.10a. Graphics for relationship between u (mm/s) and y (mm) spanwise distance at Red=7 400

t*=0.125 and x=45mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)

t*=0.25 and x=45mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)

t *=1 and x=45mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)

t *=0.125 and x=10mm

0

20

40

60

-75 75 225 375 525

u (mm/s)

y(m

m)

t *=0.25 and x=10mm

0102030405060

-75 75 225 375 525

u (mm/s) y

(mm

)

t*=1 and x=10mm

0

20

40

60

-75 75 225 375 525

u (mm/s)

y (m

m)

t*=0.125 and x=25mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)

t *=1 and x=25mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)

t *=0.25 and x=25mm

0

20

40

60

-50 150 350 550

u (mm/s)

y (m

m)


40

Figure 4.10b. Graphics for relationship between u (mm/s) and y (mm) spanwise distance at Red=7 400

As a result from looking of these graphics, it can be said that, while the

thickness / diameter ratio is increased, maximum velocity value of u decreasing. If an

example is examined closely this idea is recognized. When x is equal to 10 mm, t*

value is 0.125, umax is approximately 525 (mm/s), but for t* values are 0.25 and 1,

this velocity value is decreasing around 375 (mm/s). This decreasing is rapidly from

t* value 0.125 to t values t* 0.25 and t* 1 in comparison with between 0.25 and 1

values of t*. This means that there is not so big difference for t* values between 0.25

t*=0.125 and x=65mm

0

20

40

60

0 150 300 450

u (mm/s)

y (m

m)

t *=0.25 and x=65mm

0

20

40

60

0 150 300 450

u (mm/s)

y (m

m)

t *=1 and x=65mm

0

20

40

60

0 150 300 450

u (mm/s)

y (m

m)

t*=0.125 and x=100mm

0

20

40

60

0 150 300 450 600

u (mm/s)

y (m

m)

t*=0.25 and x=100mm

0

20

40

60

0 150 300 450 600

u (mm/s)

y (m

m)

t*=1 and x=100mm

0

20

40

60

0 150 300 450 600

u (mm/s)

y (m

m)

t *=0.25 and x=150mm

0

20

40

60

0 200 400 600 800

u (mm/s)

y (m

m)

t*=1 and x=150mm

0

20

40

60

0 200 400 600 800

u (mm/s)

y (m

m)

t*=0.125 and x=150mm

0

20

40

60

0 200 400 600 800

u (mm/s)

y (m

m)


41

and 1. Also, after x distance from the orifice plate is equal to 65mm, the increase of

velocity value rapidly in comparison with up to 65mm from the orifice plate.

The below Figures 4.11a and 4.11b present graphics which show changing of

u’v’ values with thickness / diameter ratio at specified x distance through y direction.

u’v’ values are dimensionless; it is obtained from dividing with square of free stream

velocity. This value gives us Reynolds stress value and as it is known that Reynolds

stress value shows the degree of turbulence of the flow. In fluid dynamics, the

Reynolds stresses (the Reynolds stress tensor) is the stress tensor in a fluid due to the

random turbulent fluctuations in fluid momentum. The stress is obtained from an

average over these fluctuations. Reynolds stress at any given point in a turbulent

fluid is somewhat subject to interpretation, depending upon how one defines the

average.

As seen in these graphics for same thickness of orifice plate, while going

forward through the x direction, the u’v’ value is changing. Also, it is seen that these

Reynolds stress values change direction from negative to positive along the pipe

cross-section. And it is almost to zero through the center of the pipe cross-section in

y direction around 30 mm. This means that the degree of turbulence is lowest at the

center of the pipe.


42

Figure 4.11a. Graphics for relationship between Reynolds stress (u’v’) and y (mm) spanwise distance at Red=7 400

t*=1 and x=10mm

0

20

40

60

-0,2 0 0,2

u'v'

y (m

m)

t*=0.125 and x=25mm

0

20

40

60

-2 0 2

u'v'

y(m

m)

t *=0.25 and x=25mm

0

20

40

60

-0,5 0 0,5

u'v'

y (m

m)

t *=1 and x=25mm

0

20

40

60

-0,5 0 0,5

u'v'

y (m

m)

t*=1 and x=10mm

0

20

40

60

-0,2 0 0,2

u'v'

y (m

m)

t *=0.125 and x=10mm

0

20

40

60

-1 0 1 2

u'v'

y (m

m)

t *=1 and x=45mm

0

20

40

60

-0,5 0 0,5

u'v'

y(m

m)

t *=0.125 and x=45mm

0

20

40

60

-2 0 2

u'v'

y (m

m)

t*=0.25 and x=45mm

0

20

40

60

-0,5 0 0,5

u'v'

y (m

m)


43

Figure 4.11b. Graphics for relationship between Reynolds stress (u’v’) and y (mm) spanwise distance at Red=7 400

In detail, it can be said that, while the thickness / diameter ratio is increased,

maximum value of u’v’ decreasing. If an example is examined closely this idea is

recognized. When x is equal to 150 mm, t* value is 0.125, maximum u’v’ is

approximately 2.3, but for t* values are 0.25 and 1, this value is decreasing

respectively 0.95 and 0.78. This decreasing is rapidly from t* value 0.125 to t values

t* 0.25 and t* 1 in comparison with between 0.25 and 1 values of t*. This means that

there is not so big difference for t* values between 0.25 and 1.

t*=0.125 and x=150mm

0

20

40

60

-5 0 5

u'v'

y (m

m)

t*=0.25 and x=150mm

0

20

40

60

-2 0 2

u'v'

y (m

m)

t*=1 and x=150mm

0

20

40

60

-1 0 1

u'v'

y (m

m)

t *=0.25 and x=100mm

0

20

40

60

-1 0 1

u'v'

y (m

m)

t *=1 and x=100mm

0

20

40

60

-1 0 1

u'v'

y (m

m)

t*=0.125 and x=100mm

0

20

40

60

-2 0 2

u'v'

y(m

m)

t *=0.125 and x=65mm

0

20

40

60

-2 0 2

u'v'

y (m

m)

t *=0.25 and x=65mm

0

20

40

60

-1 0 1

u'v'

y (m

m)

t *=1 and x=65mm

0

20

40

60

-0,5 0 0,5

u'v'

y (m

m)


44

In addition, the urms values are obtained graphically. The graphics for urms

values are shown below Figure 4.12a and Figure 4.12b. urms values show the data

about fluctuating velocities components. Again through the center of pipe in y

direction fluctuating velocity values are constant, and in separated flow region

fluctuating velocity component is changed as shown in below figures.

Figure 4.12a. Graphics for relationship between urms (mm/s) and y (mm) spanwise distance at Red=7400

t*=0.125 and x=10mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=0.25 and x=10mm

0

20

40

60

0 1 2

urms(mm/s)

y (m

m)

t *=1 and x=10mm

0

20

40

60

0 0,5 1

urms (mm/s)

y (m

m)

t *=0.125 and x=25mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=0.25 and x=25mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=1 and x=25mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=0.125 and x=45mm

0

20

40

60

0 2 4

urms(mm/s)

y (m

m)

t *=0.25 and x=45mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=1 and x=45mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)


45

Figure 4.12b. Graphics for relationship between urms (mm/s) and y (mm) spanwise distance at Red=7 400

Also, to see the development of flow in downstream of the orifice plate

clearly, the u, urms and u’v’ values combined at the same table along the x direction

separately. The next Figure 4.15a, Figure 4.15c and Figure 4.15b present graphics

which show changing of u, u’v’ and urms values through y direction at different x

distances for same thickness / diameter ratios.

t*=0.125and x=65mm

0

20

40

60

0 2 4

urms (mm/s)

y (m

m)

t *=0.25 and x=65mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=1 and x=65mm

0

20

40

60

0 1 2

Urms (mm/s)

y (m

m)

t*=0.125 and x=100mm

0

20

40

60

0 2 4

urms (mm/s)

y (m

m)

t *=0.25 and x=100mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t*=1 and x=100mm

0

20

40

60

0 1 2

urms (mm/s)

y (m

m)

t *=0.125 and x=150mm

0

20

40

60

0 5

urms (mm/s)

y (m

m)

t *=0.25 and x=150mm

0

20

40

60

0 2 4

urms (mm/s)

y (m

m)

t*=1 and x=150mm

0

20

40

60

0 2 4

urms (mm/s)

y(m

m)


46

Figure 4.13a. Graphics for relationship between u, u’v’ and urms and y (mm) spanwise distance at Red=7400 and different x distances for t*=0.125.

t*=0.125

0

10

20

30

40

50

60

0 1 2 3 4 5

urms (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=0.125

0

10

20

30

40

50

60

-200 0 200 400 600 800 1000

u (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=0.125

0

10

20

30

40

50

60

-3 -2 -1 0 1 2 3

u'v'

y (m

m)

x=10mm

x=25mm

x=45

x=65mm

x=100mm

x=150


47

Figure 4.13b. Graphics for relationship between u, u’v’ and urms and y (mm) spanwise distance at Red=7400 and different x distances for t*=0.25.

t*=0.25

0

10

20

30

40

50

60

-200 0 200 400 600 800

u (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=0.25

0

10

20

30

40

50

60

-1,5 -1 -0,5 0 0,5 1 1,5

u'v'

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=0.25

0

10

20

30

40

50

60

0 0,5 1 1,5 2 2,5 3

urms (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm


48

Figure 4.13c. Graphics for relationship between u, u’v’ and urms and y (mm) spanwise distance at Red=7400 and different x distances for t*=1.

t*=1

0

10

20

30

40

50

60

-200 0 200 400 600 800

u (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=1

0

10

20

30

40

50

60

-1 -0,5 0 0,5 1

u'v'

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm

t*=1

0

10

20

30

40

50

60

0 0,5 1 1,5 2 2,5

urms (mm/s)

y (m

m)

x=10mm

x=25mm

x=45mm

x=65mm

x=100mm

x=150mm


49

Finally, it is obtained that while going through on the x direction; u values

first are decreased up to 100 mm then increased, Reynolds stress values are increased

and urms values are increased. These results can be said same for three different case

that changing of thickness / diameter ratios of the orifice plate.

5. CONCLUSIONS Mustafa OĞUDAY

50

5. CONCLUSIONS

This study is primarily conducted to investigate the flow characteristics through

the orifice plate inserted in a pipe in turbulent flow regimes by using PIV technique.

While the orifice/pipe diameter ratio, which is β=0.6, is kept constant, the orifice plate

thickness/diameter ratio t* is varied from 1/8 to 1 through the results being done

turbulent flows. The Reynolds number is varied from 7 400 to 37 000 based on pipe

diameter. In order to demonstrate the characteristics of the flow through the orifice

plate, the formation and development of flow in side view plane downstream of the

orifice plate, 350 images of instantaneous velocity fields were taken. So, in order to

understand the flow characteristics in the region of the orifice plate downstream, the

PIV technique is applied to obtain time- averaged flow data in the side-view laser

planes.

The flow data backside of orifice plate in side-view planes are presented using

time-averaged velocity vector map, streamline patterns, vorticity contours. In addition,

variation of time-averaged velocity vectors along a specific line is also presented

graphically. From the time-averaged flow data the behavior of the flow in backside of

orifice plate can be seen clearly, it is known that when the flow passes from the orifice

plate the flow structure changes in comparison with upstream of flow structure. When

looking these velocity maps, streamline patterns and vorticity contours maps general

opinion can be seen clearly. From this knowledge some results are obtained.

In turbulent flow, as the thickness of the orifice plate increases, the flow

separation occurs in the orifice bore. Namely, both detachment and reattachment of flow

occur before flow leaves the orifice plate as seen in result and discussion part of this

study.

One of the results of these study is, when the t * is increased separated flow

region occurs further from the orifice plate in x-direction. In addition the form of that

region becomes longer and thinner. The length of separated flow region increases with

increasing the Reynolds number.

Secondly, when the t* value is increased from 1/8 to 1, vena contracta occurs

closer to orifice plate, in turbulent flows as seen in this study results. However, when

5. CONCLUSIONS Mustafa OĞUDAY

51

the Reynolds number is increased, the vena contracta occurs further from the orifice

plate.

Also, the effects of orifice plate on the characteristics of flow are also possible in

terms of the velocity vectors of the flow field. It is known that directions of velocity

vectors are parallel to the central axis of the pipe before the orifice plate. And their

directions change through the orifice plate. By looking time-averaged velocity vectors,

it can be said that while the thickness/ diameter ratio value is increased, the length of

velocity jet increases.

In addition to these results, in order to investigate the flow characteristics

quantitatively, the flow field was divided into 54 intervals in the vertical direction. So,

variation of time-averaged velocity vectors along a specific line is also presented

graphically. As seen in these graphics for same thickness of orifice plate, while going

through the x direction, the u, u’v’ and urms values are decreasing naturally. In detail, it

is seen that these Reynolds stress values change direction from negative to positive

along the pipe cross-section. And it is almost to zero through the center of the pipe

cross-section in y direction around 30 mm. This means that the degree of turbulence is

lowest at the center of the pipe. Also, it can be said that, while the thickness / diameter

ratio is increased, maximum value of u’v’ decreasing. For urms values again through the

center of pipe in y direction fluctuating velocity values are constant, and in separated

flow region fluctuating velocity component is changed.

Finally, in order to see the development of flow in downstream of the orifice

plate clearly; u, urms and u’v’ values combined at the same table along the x direction

separately.

52

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55

CURRICULUM VITAE

Mustafa OĞUDAY was born in Kayseri in June 1979. He graduated from

Turkish Air Force Academy Aeronautical Engineering in August 2000. He started to

pilot training at 2nd Air Base Commandership/İzmir in same year. He finished pilot

training and started Maintenance Management training at Turkish Air Force Expertise

Training School in September 2000. He has started his Master of Science education at

the mechanical engineering department of Çukurova University in September 2005. He

has been working as a Maintenance Management Officer at 10th Tanker Air

Base/Incirlik since 2003.

Çukurova university institute of natural and applied ... · türbülanslı akışta orifis...

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