Physics behind vortex flowmeter by flow vizualization method

1. Department of Mechanical Engineering
Government College of Engineering , Aurangabad
(An Autonomous Institute of Government of Maharashtra)
(2014-2015)
1
Guided by:
Prof.M.S Harne
Submitted By:
Apurva Ashok Kulkarni
(ME12F11F008)
Dissertation part -II
ON
“STUDY OF VORTEX SHEDDING BEHIND TRAPEZOIDAL BLUFF BODY
BY FLOW VISUALIZATION METHOD”
“In Pursuit of Global Competitiveness”

2. OUTLINE
1. Introduction.
2. Literature Survey.
3. System Development.
4. Performance Analysis.
5. Conclusion.
6. Future scope.
7. References.

3. 1.INTRODUCTION
1. In the present study specially designed Experimental set up is
fabricated to study flow visualization experiments with bluff body
placed inside 50 mm diameter circular pipe.
2. Trapezoidal shape bluff body is used with blockage ratio of 0.27.
3. Dye injection technique is used to visualize the complex vortex
formation mechanism behind bluff body.
4. The dye used is concentrated KMNO4.
5. The study improves the understanding of complex vortex formation
mechanism in the design of vortex flow meter.
6. Various wake parameters like Strouhal number, vortex formation
length and wake width are calculated.

4. STUDY OF VORTEX SHEDDING BEHIND TRAPEZOIDAL
BLUFF BODY BY FLOW VISUALIZATION METHOD
1. Flow Visualization is a powerful tool in development and understanding
of fluid dynamics.
2. The unique advantage of this technique is that certain properties of the
flow field become directly accessible to visual perception and the insight
into a physical process becomes clearer.
3. Most fluids are transparent media and their motion remains invisible to
the human eye during direct observations. However, the motion of such
fluids can be recognized by making use of techniques by which the flow is
made visible and such techniques are called flow visualization
techniques.
4. It is also possible to derive quantitative data from the flow pictures
obtained by such techniques. Information about the complete flow field
can be arrived without physically interfering with fluid flows.
Why?

5. What is Vortex Shedding ??
•A Vortex sheds off an obstacle at a defined point
•As velocity (Re number) increases this point will move along contour

6. 2. OBJECTIVE
1. Calculation of vortex formation length.
2. Identification of strouhal Number.
3. Identification of wake width.
4. Identification of Reynolds number.
5. Identification of optimum position of pressure sensor.

7. 1) Strouhal Number:-
F=frequency of vortex shedding (Hz)
d=width of bluff body (m)
v= Average flow velocity(m/s)
2) Vortex formation length(L’):-
The stream wise distance between the front separation point
and the point where the vortex is about to shed from the
shear boundary layer, is taken as the vortex formation length
(L’).
3) Wake width(W):- Wake width is defined as the maximum
vertical distance between the two shear layers.

8. FIGURE SHOWING WAKE WIDTH(W) AND
VORTEX FORMATION LENGTH(L’)

9. VORTEX HISTORY AND PRINCIPLE
Extract from Leonardo da
Vinci’s sketch book made in
1513
A flag in the wind is moving because
of shedding vortices behind pole

10. VORTEX MEASUREMENT
f = Vortexfrequency
V = Volumeflow
Bluff Body
f ~ V
DSC Sensor
Transmitter
𝑆𝑡 =
𝑓𝐷
𝑈 𝑚
Where
𝑓 - vortex shedding frequency.
D - bluff body diameter
𝑈 𝑚 - mean free-stream velocity.

11. THE KARMAN STREET IN A VORTEX
METER

12. VARIOUS BLUFF BODY SHAPES
Ring Triangular Conicalcircular RingTrapezoidal

13. 13#
VORTEX FLOWMETER PRINCIPLE
Basic Flow Equation: Q = A * V
Flowing Velocity of Fluid: V = (f * d) / St
f = Shedding Frequency
d = Diameter of Bluff Body
St = Strouhal Number (Ratio between Bluff Body Diameter and Vortex
Interval)
A = Area of Pipe

14. STROUHAL NUMBER VARIATION WITH
REYNOLDS NUMBER

15. Primary Element
Vortex Shedder Sensor
Vortex Flow meter
Secondary Element
Signal Processing Signal Converter
PARTS OF VORTEX FLOW METER

16. UNIQUE FEATURES OF VORTEX
FLOWMETER
1. No Moving parts.
2. Large Turndown ratio.
3. Low Maintenance.
4. High operating pressure & Temperature (30 bar,
450° C .
5. Low Cost.
6. Specially Suitable for Steam.
7. Good Accuracy (± 0.75 - 1.5% ).
8. Versatility - Same meter can be used in any
compatible medium.

17. SENSORS USED

18. 2.LITERATURE REVIEW
SR. NO. NAME OF THE SCIENTISTS OUTCOMES
01.
Bernard
(1908)
observed alternate precision of eddies behind a
circular cylinder in water, based on visible dimples on
water surface.
02.
Von Karman
(1911)
03.
Bearman
(1969)
examined, the flow around a circular cylinder over the
Reynolds number range 105 to 7.5 x105, Narrow-band
vortex shedding has been observed up to a Reynolds
number of 5.5 x 105, i.e. well into the critical regime.
04.
C. J. Baker
(1974)
investigated experimentally the formation of
horseshoe vortex around the base of a cylinder by a
separating laminar boundary layer.

19. SR. NO. NAME OF THE SCIENTISTS OUTCOMES
05.
Igarashi
(1978)
investigates on the flow characteristics around a
circular cylinder .Flow visualization, hot-wire
measurement of the wake flow and the distribution
of the static pressure coefficients around the
cylinder have been made.
06
Sadeh and Brauer
(1980)
conducted a diagnostic visualization study of
turbulence in stagnation flow around a circular
cylinder to gain physical insight into the coherent
structure of turbulence in flow around a bluff body
advanced by the vorticity-amplification theory.
08. Szepessy and Bearman (1990) have studied aspect ratio effects on the vortex
shedding flow from a circular cylinder by using
moveable end plates
09. Igarashi (1995) confirmed the equation is applicable to the vortex
shedder having a low opening ratio

20. SR. NO. NAME OF THE SCIENTISTS OUTCOMES
10 Blackburn and Melbourne
(1996)
conducted wind tunnel experiments to examine the
effect of grid-generated turbulence on lift forces at
sections of a circular cylinder.
11 Hans et al. (1998) investigates vortex shedding flow meters coupled with
a detection of the vortex frequency by an ultrasound
barrier behind the bluff body.
12 Igarashi (1999) experimentally studied three different bluff bodies
(trapezoidal, cylinder with a slit and triangular
semicircular cylinder). The most important outcome
of his work was circular cylinder with a slit as an
improved vortex generator.
13 Miau et al. (2002) employed dye visualization technique to understand
the vortex shedding mechanism with a ring shaped
bluff bodies. Flow visualization images revealed that
the presence of pipe wall affects the vortex shedding
mechanism and for blockage ratio above certain
values, vortex shedding was completely inhibited

21. SR. NO. NAME OF THE
SCIENTISTS
OUTCOMES
14 Lavante et al. (2003) investigates the problem of accurate determination of
volumetric flows by means of vortex-shedding flow meter
in the case of shape changes and deviations of the
geometry from the original specifications due to
manufacturing tolerances and imperfections were
studied.
15 Zang et al. (2006) suggested a new method in which mass flow rate can be
directly measured based on the vortex shedding principle
16 Pankanin et al. (2007) presented a method of quantitative flow visualization of
the Karman street. Image processing creates the ability
for quantitative evaluation of the phenomena and
enables the determination of geometric parameters of
the vortex street
17 Peng et al. (2008) carried out the experimental studies on the Strouhal
number for flow past dual triangulate bluff bodies in a
Results are presented of an experience instrument
evaluation of the Strouhal number of nine dual
combinations based on triangulate bluff body geometries
of different size for a range of separations

22. SR. NO. NAME OF THE SCIENTISTS OUTCOMES
18 Venugopal et al. (2010) conducted experimental investigations on vortex
flow meter with the differential wall pressure
measurement method.
19 Venugopal et al. (2011) carried out experimental and numerical
investigations with various bluff body shapes to
identify an appropriate shape which can be used for
vortex flow meter application
20 Venugopal et al. (2013) states, piezoelectric sensors are one of the most
widely used sensors for vortex flow meter
application due to their low cost.
21 Venugopal et al. (2014) employed piezoelectric and transient differential
pressure sensors for vortex flow meter application.
This study evaluates the performance of these two
techniques under fully developed and disturbed
flow conditions.

23. RESEARCH GAP
1. By referring various research papers on vortex flowmeter most of
them described the, Effect of blockage ratio on performance of
vortex flowmeter and very few have explored the dynamics of
vortex shedding i.e. How vortex are formed, What is vortex
formation length ,wake width , strouhal number ,where the
sensor should be located and what is the effect of these
parameters on accuracy of vortex flowmeter by using trapezoidal
shape bluff body.

24. PROBLEM IDENTIFICATION
 Flow visualization helps in obtaining following parameters:
1. Vortex shedding frequency (Strouhal number)
2. Vortex formation length
3. Wake width
 Strouhal number is computed either by manually counting the number of
vortices being shed or from image processing. Vortex formation length is
required to know the location of the sensor to be placed.
 Flow visualization study helps us to understand the flow physics in the
wake region of the bluff body. Reynolds number at which vortex shedding
starts can be found out using flow visualization. Size of the vortices can be
computed by processing the images obtained from flow visualization.
 Behaviour of different bluff bodies with different shapes and sizes can be
studied from vortex shedding perspective.

25. 3.EXPERIMENTAL SET UP
VORTEX
CORIOLIS
TANK
SUMP

26. SUMP
CORIOLIS FLOW
METER
ELECTRO
MAGNETIC
FLOW METER
VORTEX FLOW
METER
TANK

27. EXPERIMENTAL SET UP

28. INLET AND OUTLET REQUIREMENT
A – INLET RUN
B – OUTLET RUN
1 – REDUCTION
2 – EXTENSION
3 – 90 DEGREE ELBOWS
4 -- 90 DEGREE ELBOWS- DIMENSIONAL
5-- 90 DEGREE ELBOWS
6 – CONTROL VALVE
Always consider the worst case disturbance

29. EXPERIMENTAL SET UP DETAILS
• Tank
• Butterfly valve
• Globe valve
• Flow conditioner
• Vortex flow meter
• Electromagnetic flow meter
• Coriolis Flow meter
• Pump
• sump

30. CYLINDRICAL TANK
Volume of Tank/Capacity of Tank V= π r^(2)h
= 3.14*(0.3*0.3)*0.775
=0.22 m^(3)
=220 lit
Material of Tank = Stainless Steel(SS304)

31. BLUFF BODY OR VORTEX SHEDDER
 IT is the heart of the vortex flow meter. The strength,
linearity and stability of the vortex are defined by the shape,
blockage and other geometrical parameters of the vortex
shedder.
Fig. 6. Trapezoidal shape Bluff Body

32. Vortex Flow Meter
• Manufactured vortex flow meter Specification:-
• Meter Size DN 50
• Minimum Flow 1.52 m3/h
• Maximum Flow 61.598 m3/h
• Material (sensor) * SS 1.4408 / CF3M
• Process connection* PN 40 EN 1092-1 B1 / 1.4404/316L Flange

33. Mitsubishi Flow conditioner
Flow Conditioner is used to eliminate swirl.
it is inserted upstream of the flow meter to reduce the length of straight pipe required
FLOW CONDITIONER

34. Electromagnetic Flow meter
• It is used to measure the velocity of fluid

35. Coriolis Flow Meter
• Flowmeter : Promass 40E
• Flow Principle Coriolis (Promass)
• Meter Size DN 50
• Minimum Flow 0 m3/h
• Maximum Flow 70.478 m3/h
• Material (sensor) * SS 1.4539/904L, ext.temp.
• Process connection* PN 40 EN 1092-1 B1 / 1.4404/316L Flange

36. 9. Pump
The water from the flow meter is collected into the ump and
re-circulated to overhead tank by using 0.5 HP pump. Since
the experiment involves contaminating the working fluid
with a dye, it becomes necessary to change the water in
the reservoir from time to time.
10. Small tank for die.
The dye used was concentrated KMNO4 (Potassium
Permanganate) solution. The dye was injected into the flow
from two openings of 0.8mm diameter, at the center of the
length of the vortex shedder
•

37. Reynolds Number
Re=(Inertia Force/Viscous Force)
Re=ρνD/µ
Where:ρ=Density of fluid(kg/m3)
v=Mean vel of fluid(m/s)
D=Dia of pipe(m)
µ= Dynamic viscosity(Kg/ms)

38. 4.PERFORMANCE ANALYSIS
1. The images were taken from the flow visualization videos, which were processed using
MATLAB software.
2. The frequency is obtained from the video by finding out the number of vortices passing
through an appropriate point in the image in a unit second
3. The bluff body width (d) is taken as the characteristic length and the average flow velocity
(Um) as the characteristic velocity.
4. Non dimensional strouhal number St can be calculated using the relation (1)
5. The stream wise distance between the front separation point and the point where the vortex
is about to shed from the shear boundary layer, is taken as the vortex formation length (L’).
6. The vortex formation length and the wake width were calculated by averaging the respective
quantities obtained from all the separate images extracted from the videos analysis.

39. Matlab program for wake width
%finding wake width
clc;
clear;
centroid_prev=zeros(2,24);
centroid_next=zeros(2,24);
x1=zeros(1,24);
y1=zeros(1,24);
x=zeros(1,24);
y=zeros(1,24);
t=0;
t1=0;
for c=50:50:1200
b=c/50;
centroid_prev(1,b)=c;
fprintf('Region %d',b);

40. fprintf('==================n');
z=0;
for i=1:25
%read background and main image and subtract to be left with just dye
if i<10
filename=sprintf('2012_12_07_0031_000%d.jpg',i);
elseif i<100
filename=sprintf('2012_12_07_0031_00%d.jpg',i);
else
filename=sprintf('2012_12_07_0031_0%d.jpg',i);

41. end
A=imread(filename);
B=imread('background.jpg');
I=imsubtract(B,A);
%figure,imshow(I);
hold on;
I=rgb2gray(I);
I=im2bw(I,0.28);
I=bwareaopen(I,500);
I=imfill(I,'holes');
SE=strel('disk',6);
I=imclose(I,SE);
%figure,imshow(I)
%hold on;
seD = strel('diamond',1);
•

42. N = imerode(I,seD);
M = imerode(N,seD);
M=imerode(M,seD);
%clear border
M=imclearborder(M);
figure,imshow(M);
%L1 = bwlabel(M);
%using regionprops to identify the properties of our region
s=regionprops(M,'Centroid');
for k=1:numel(s)
if s(k).Centroid(2)<360
if s(k).Centroid(1)<(c+50)
if s(k).Centroid(1)>c
centroid_next(1,b)=s(k).Centroid(1);

43. centroid_next(2,b)=s(k).Centroid(2);
vx=(centroid_next(1,b)-centroid_prev(1,b))*12*0.1047*0.001;
%vy=(-centroid_next(2,b)+centroid_prev(2,b))*12*0.1047*0.001;
x1(1,b)=x1(1,b)+centroid_next(1,b);
y1(1,b)=y1(1,b)+centroid_next(2,b);
z=z+1;
if z==0
fprintf('**');
else
t=x1(1,b)/z;
t1=y1(1,b)/z;
plot(t,t1,'r*');
hold on;
end
end
end
end
end

44. Matlab Images for Processing

45. MATLAB INPUT IMAGES

46. MATLAB OUT PUT IMAGES

47. MATLAB INPUT IMAGES

50. CFD
SOLVER
Type-pressure based.
Velocity formation -absolute.
Time –steady.
2D space- planar.
Gravity on with y axis -9.81 m/s^2.

51. MODEL
All model off only viscous-laminar or sapalart-allmaras(1eq).
MATERIAL :Water liquid.
BOUNDARY CONDITION
Inlet -1m/s.
Reference value – compute from inlet.
Solution method-scheme –simple or pisco.
Solutioninitialization –computes from inlet and initialize.
Run calculation
Number of interlation-500.
Reporting interval-10.

52. Blockage ratio =width of bluff body/dia of pipe
d/D=13.5/50=0.27mm
f= 0.04 Hz, d = 13.5mm
v= 1m/s
reynold number =5.84*10^4
st=0.00054.

60. SR.
N0.
Velocity
(m/s)
Reynolds Frequency
(Hz)
Strouhal Discharge
(m3/hr)
1 0.01 500 0.04 0.2 2*10^(-5)
2 0.02 1000 0.06 0.4 4*10^(-5)
3 0.03 1500 0.08 0.6 6*10^(-5)
4 0.04 2000 0.01 0.8 8*10^(-5)
5 0.015 750 0.05 0.3 3*10^(-5)
6 0.025 1250 0.07 0.5 4*10^(-5)
7 0.035 1750 0.09 0.7 7*10^(-5)

61. 0
2
4
6
0 1000 2000 3000
L'/D
Re
L'/d vs Re
0
0.2
0.4
0.6
0.8
0 2000 4000
st
Re
St vs Re
0
0.5
1
1.5
2
2.5
0 1000 2000 3000
w/d
Re
W/d vs Re

62. Sr.No Parameters Experimental
result
Matlab
result
CFD result %Error
1 St. No (St ) 0.3 0.28 6.6
2 Vortex
Formation
length(L’)
4 3.9 2.5
3 Wake
Width(W)
2 1.9 5
RESULT ANALYSIS

63. 5.CONCLUSION
The conclusions drawn from present study are:
• 1. The strouhal number, vortex formation length and
wake width are dependent on each other. The wake
width is found to have an opposite nature to that of the
vortex formation length. The wake width determines the
degree of shear layer interaction, and hence the Strouhal
number.
• 2. Sensor should be located at the vortex formation
length so as to obtain high amplitude signal.

64. FUTURE SCOPE
• New Shedder Shapes like cylindrical, triangular ,Cylinder with
slit can be Deigned
• Instead of single bluff body dual bluff body can be used to
improve accuracy of flow measurement
• Different types of sensors can be used like piezoelectric
,capacitive sensor