Experiment 2 (Free and Forced Vortex)

UNIVERSITI TEKNOLOGI MARA FAKULTI KEJURUTERAAN KIMIA THERMOFLUIDS LABORATORY (CGE 536)

GROUP MEMBERS

EXPERIMENT DATE PERFORMED SEMESTER PROGRAMME GROUP No. 1 2 3 4 5 6 7 8 9 10 11 12 13

: AMIRA BINTI KORMAIN (2014851022) FARHAN HAIRI BIN KASIM (2014204678) MOHD ZAIDI BIN MOHD RADZALI (2014678172) NURULTHAQIFAH BINTI BAHARUM (2014870248) : FREE AND FORCED VORTEX : 4TH APRIL 2015 : 3 : EH 243 : GROUP 8

Title Abstract/Summary Introduction Aims/Objectives Theory Apparatus Procedures Result Calculations Discussion Conclusion Recommendations References Appendices TOTAL MARKS Remarks:

Allocated Marks (%) 5 5 5 5 5 10 10 10 20 10 5 5 5 100

Marks

Checked by: Date: TABLE OF CONTENT Contents Abstract 1.0 Introduction 2.0 Objectives

Pages 3 3 4

3.0 Theory 4.0 Apparatus 5.0 Experimental Procedures 6.0 Results 7.0 Sample Calculations 8.0 Discussion 9.0 Conclusion 10.0 Recommendations 11.0 References 12.0 Appendices

4 7 9 11 19 20 21 22 22 22

ABSTRACT The aim for this experiment are divided into two parts, free and forced vortex. In free vortex, the objective are to study the surface profile and speed of the vortex and also to find the relationship between the surface profile and speed of the vortex. For forced vortex, the objetive are to study the surface profile and angular velocity of the voertex and also to find the relationship between surface profile and total head. For free vortex experiment, orifices with different diameters are used to observe and study the free vortex. It can be obesrved that as the radius of the orifice increases, the velocity of water decreases and bigger orifice will

produce greater vortex. For forced vortex experiment, it involves the use of paddle at the bottom of the tank to create forced vortex. It can be observed that as the angular velocity increase, the height from top of measuring gauge to bridge , h, also increase. As the angular velocity increase, the slope of the curve also increase because of the stream function formed in forced vortex is parabolic in nature. As conclusion, all the objectives given in this experiment were successfully achived.

1.0 INTRODUCTION The equipment mainly used in the experiment is the SOLTEQ Free and Forced Vortex (Model: FM24) which is designed to produce and measure the characteristics of free and force vortices. The orifice discharge accessory enables full analysis of the flow through four different orifices over a range of flow rates. Vortex is the rotation of fluid elements around a common center. Mostly the fluid flows in a spinning motion about an imaginary axis, straight or curve where these motion patterns are called vortical flows. There are two types of vortices, i.e. free and forced. The fluid (or gas) circles around a center in a forced vortex, whilst in a free vortex, the medium spirals towards the center. In industry sector and the real world, the applications of the vortex flow can be seen in various areas like in turbine design, natural phenomenon and also in creating safety against natural disaster. Free vortex formed when water flows out of a vessel through a central hole in a base of a tank in which the degree of the rotation being dependent on initial disturbance. In the free vortex flow, the fluid mass rotates without any external force. The rotation cause by either by internal action or due to some rotation imported previously. Throughout this experiment, the free vortex is created by using rotating plate. For instance, the free vortex motion is flow through an opening at the bottom of a shallow vessel where the speed and rate of rotation of the fluid are the greatest near the center. Forced vortex motion is caused by the external forces on the fluid such as the impeller of a pump. In this very experiment, the forced vortex flow is created by using the rotating plate with the addition of paddle. The speed of the forced vortex is zero at the center and keeps increasing proportional to the distance measured from the center. Both free and forced vortex exhibit minimum pressure minimum at the center, however free vortex has a much lower minimum pressure compared to forced vortex. During the forced vortex motion, the

fluid mass is made to rotate by external source of power which it exerts a constant torque on the fluid mass and caused it to rotate with a constant angular velocity. 2.0 OBJECTIVES The experiment was conducted in order to fulfill few objectives. They are divided into free vortex and forced vortex. In free vortex, the objectives are to study the surface profile and speed of the vortex and also to find the relationship between the surface profile and speed of the vortex. On the other hand, in forced vortex, the objectives are to study the surface profile and angular velocity of the vortex and also to find the relationship between surface profile and total head. 3.0 THEORY A vortex is a spinning, often turbulent (violent), flow of fluid. Any spiral motion with closed streamlines is vortex flow where the motion of the fluid swirling rapidly around a center is known as vortex. The speed and rate of rotation of the fluid in a free (irrotational) vortex are greatest at the center, and decrease progressively (little by little) with distance from the center, whereas the speed of a forced (rotational) vortex is zero at the center and increases proportional to the distance from the center (“Theory of a Vortex”). There are two types of vortex flow which are free vortex flow and forced vortex flow.

Figure 1: Free and Forced Vortex Flow Free vortex

The essential characteristic of free vortex in ideal fluid is that it does not require the application of external energy or any other addition or destruction of energy in the flow field. In such cases, the absence of friction would make it impossible to create or destroy the vortex motion. The motion in the fluid might be permanent flow pattern and the velocity of the fluid element that instantaneously passing through a given point will be constant with the time. Some of the examples of free vortex are the flow of liquid through a hole at the bottom of the container, the flow of liquid around a circular bend in pipe and the flow of fluid in a centrifugal pump casing (Pattison, n.d.). The water moves spirally towards the center with a streamline motion which by neglecting losses caused by the viscosity, the energy unit per mass will kept constant. The fluid particles move in circle about a point in the free vortex flow. The only-trivial velocity component is tangential where this tangential speed varies with radius in order the same circulation is maintained. All the streamlines are concentric circles about given point where the velocity along each streamline is inversely proportional to the distance from the center. In the non-technical terms, the fluid near the center of the vortex will circulate faster. At the same time, the inner streamline have a shorter distance to travel to complete the ring. Based on the vortex profile for all diameter of orifice and gradient of the graph can be calculated using the equation: 2

( )( r1 )

X=

K 2g

2

Where; X

= pressure head/ depth of the pitot tube

g

= gravitational acceleration

r

= radius Based on the velocity which can be calculated from the pitot tube reading and the

radius profile:

V =(2 gH )0.5 Where; V

= velocity

g

= gravitational acceleration

H

= pitot tube difference Thus, theoretically, the velocity can be calculated using the equation:

V=

K r

Forced vortex In contrary with free vortex, the fluid motion in forced vortex circles around the center where the speed and rate of rotation of the fluid is the greatest at the center and decrease progressively as it goes away from the center. Few examples of forced vortex motion are the vertical cylinder containing liquid rotated about its central axis with constant angular velocity, the flow of liquid inside the impeller of a centrifugal pump and flow of water through the runner of a turbine (Pattison, n.d.). Throughout the experiment, the forced can be created by rotating the body containing the fluid or by the addition of paddle in the fluid. Streamlines for such flow shall be concentric circles and the total energy is constant along a streamline. The equation for the forced vortex can be created by applying Newton’s law to a fluid element and assuming there is no shear stress acting on the fluid which is no relative motion between adjacent particles. In conclusion, the resulting equation can be expressed as: 2 2

w r ∆ h=h−h0= 2g Where; h

= initial (non-rotating) surface height of the fluid

h0

= height on the axis

ω

= angular velocity, radian/second

r

= radius of the cylinder

g

= gravitational acceleration

4.0 APPARATUS

Figure 2: SOLTEQ Free and Forced Vortex Model FM42

Figure 3: Profile measuring gauge

Figure 4: Paddle

Figure 5: Pitot tube

Figure 6: Orifices

5.0 EXPERIMENTAL PROCEDURES General Start-up Procedures 1. The study bench was placed on the hydraulic bench. 2. The inlet and outlet hose was set up. 3. The stand of the equipment was adjusted to reach the horizontal position. General Shut-down Procedures 1. The valves were closed and the pump was switched off. 2. The orifices, paddle and other accessories were removed from the cylindrical vessel.

Experiment 1: Free Vortex 1. The general start-up procedures were performed.

2. An orifice with a diameter of 24mm was placed on the base of a cylinder tank. 3. The output valve was closed and the inlet 3-way valve was adjusted to let the water flows into the tank from two pipes with 12.5 mm diameter. The water could flow out through the orifice. 4. The pump was switched on and the control valve on the hydraulic bench was opened slowly until it reached the tank limit. The water level was maintained by adjusting the control valve. 5. The vortex profile was collected once the water level was stable by measuring the vortex diameter for several planes by using the profile measuring gauge. 6. The profile measuring gauge was pushed down until the both of sharp point touch the water surface. 7. The measured height, h (from the top of the profile measuring gauge to the bridge) and the value of a (distance from the bridge to the surface of the water level (bottom level of the cutout)) were measured. 8. In order to measure the velocity, pitot tube was used by sinking it into the water at the depth of 5 mm from the water surface. The depth of the pitot tube in the water, H was measured. 9. Step 3-8 were repeated for another three orifices with diameter 12 mm, 16 mm and 8 mm respectively. 10. The coordinates of vortex profile for all diameter of orifice was plotted in a graph the gradient of the graph was calculated by using the formula below :

X=

2

K 2g

∙

1 2 r

11. Graph of velocity was also plotted which was calculated from the pitot tube reading versus the radius of the profile. V = (2gH)0.5 Theoretically, the velocity was calculated by using the following equation: K V= r Experiment 2: Forced Vortex 1. 2. 3.

Perform the general start-up procedures. A closed pump with two pedals was placed on the base of the cylinder tank. The output valve was closed and the inlet 3-way valve was adjusted to let the water flows into the tank from two pipes with 9.0 mm diameter. The water could flow out through another two pipes with 12.5mm diameter.

4.

It was ensured that the water flow out from the tank with the siphon effect by raising

5.

the hose to above the water level in the tank. The outlet hose was filled with water before letting the water to flow into the sump

6.

tank in the hydraulic bench The angular speed of the pedals was measured by counting the number of circles in a

7. 8. 9. 10.

certain times. The surface probe was pushed down until the sharp point touch the water surface. The measured height, h0 (from top of the measuring gauge to bridge) was recorded. Step 4 – 8 were repeated with different volumetric flow rate. The coordinates of vortex profile for different angular velocity was plotted.

11.

The calculated vortex profile was plotted in the same graph as they relate as

h = h0 +

ω2 2g

r2

6.0 RESULTS Part A: Free Vortex a. Orifice diameter = 24 mm Distance from bridge to water surface, a = 225 mm Table 1: Data obtained for 24 mm orifice diameter Pressure Diamete r at centre, D (mm)

Measured height, h (mm)

Pitot tube head

head / Depth of

difference

the pitot

, H (mm)

tube, X

Velocity, V (mm/s)

Radius,

1/r2

2

r

2

r (mm)

(mm )

(1/mm2 )

(mm) 72.0

82.0

10.0

23.0

442.94

36.0

1296.00

77.0

95.0

9.0

10.0

420.21

38.5

1482.25

84.0

100.0

8.0

5.0

396.18

42.0

1764.00

7.72x1 0-4 6.75x1 0-4 5.67x1 0-4

Pressure head against 1/r2 f(x) = 9x - 5.33

Figure 7: Graph of pressure head against 1/r2 for a 24 mm orifice diameter Table 2: Difference between actual and theoretical velocity for 24 mm orifice diameter Radius, r (mm) 36.0 38.5 42.0

Actual velocity (mm/s) 442.94 420.21 396.18

Theoretical velocity (mm/s) 11.67 10.91 10.01

Velocity against radius

Actual velocity Theoretical velocity

Figure 8: Graph of velocity against the radius of the profile for 24 mm orifice diameter b. Orifice diameter = 16 mm

Distance from bridge to water surface, a = 230 mm Table 3: Data obtained for 16 mm orifice diameter Pressure Diamete

Measured

r at centre, D (mm)

height, h (mm)

Pitot tube

head /

head

Depth of

difference

the pitot

, H (mm)

tube, X

Velocity, V (mm/s)

2

Radius,

r

r (mm)

(mm2)

1/r2 (1/mm2 )

(mm) 48.0

77.0

11.0

23.0

464.56

24.0

576.00

49.0

85.0

9.0

15.0

420.21

24.5

600.25

50.0

97.0

7.0

3.0

370.59

25.0

625.00

1.74x1 0-3 1.67x1 0-3 1.60x1 0-3

Pressure head against 1/r2 f(x) = 10x - 6.33

Figure 9: Graph of pressure head against 1/r2 for a 16 mm orifice diameter Table 4: Difference between actual and theoretical velocity for 16 mm orifice diameter Radius, r (mm) 24.0 24.5 25.0

Actual velocity (mm/s) 464.56 420.21 370.59

Theoretical velocity (mm/s) 18.46 18.08 17.72

Velocity against radius

Actual velocity Theoretical velocity

Figure 10: Graph of velocity against the radius of the profile for 16 mm orifice diameter c. Orifice diameter = 12 mm Distance from bridge to water surface, a = 226 mm Table 5: Data obtained for 12 mm orifice diameter Pressure Diameter

Measured

at centre,

height, h

D (mm)

(mm)

Pitot tube

head /

head

Depth of

difference,

the pitot

H (mm)

tube, X

Velocity,

Radius,

1/r2

r2 2

V (mm/s)

r (mm)

(mm )

(1/mm2 )

(mm) 46.0

81.0

9.0

23.0

420.21

23.0

529

47.0

90.0

8.0

14.0

396.18

23.5

552.25

59.0

101.0

7.0

3.0

370.59

29.5

870.25

1.89x103

1.81x103

1.15x103

Pressure head against 1/r2 f(x) = 10x - 6.67

Figure 11: Graph of pressure head against 1/r2 for a 12 mm orifice diameter Table 6: Difference between actual and theoretical velocity for 12 mm orifice diameter Radius, r (mm) 23.0 23.5 29.5

Actual velocity (mm/s) 420.21 396.18 370.59

Theoretical velocity (mm/s) 19.26 18.85 15.01

Velocity against radius

Actual velocity Theoretical velocity

Figure 12: Graph of velocity against the radius of the profile for 12 mm orifice diameter d. Orifice diameter = 8 mm

Distance from bridge to water surface, a = 240 mm Table 7: Data obtained for 8 mm orifice diameter Pressure Diamete

Measured

r at centre, D (mm)

height, h (mm)

Pitot tube

head /

head

Depth of

difference

the pitot

, H (mm)

tube, X

Velocity, V (mm/s)

2

Radius,

r

r (mm)

(mm2)

1/r2 (1/mm2 )

(mm) 29.0

67.0

7.0

23.0

370.59

14.5

210.25

33.0

74.0

6.0

16.0

343.10

16.5

272.25

34.0

85.0

6.0

5.0

343.10

17.0

289.00

4.76x1 0-3 3.67x1 0-3 3.46x1 0-3

Pressure head against 1/r2 f(x) = 9x - 3.33

Figure 13: Graph of pressure head against 1/r2 for a 8 mm orifice diameter Table 8: Difference between actual and theoretical velocity for 8 mm orifice diameter Radius, r (mm) 14.5 16.5 17.0

Actual velocity (mm/s) 370.59 343.10 343.10

Theoretical velocity (mm/s) 28.98 25.47 24.72

Velocity against radius

Actual velocity Theoretical velocity

Figure 14: Graph of velocity against the radius of the profile for 8 mm orifice diameter Part B: Forced Vortex Table 9: Data for forced vortex experiment obtained and calculated value Distance from centre (mm) 0 30 70 110 No of revolutions

h0 (mm) 1st

2nd

3rd

Measured

Theoretical

Measured

Theoretical

Measured

Theoretical

62 63 67 73

62 63.55 69.99 80.38

77 78 80 86

77 78.58 83.17 93.82

91 94 96 101

91 94.62 99.36 109.31

33

34

35

velocity

3.46

3.56

3.67

(rad/s) LPM

10.00

10.59

12.86

in 60s Angular

Height from top of measuring gauge to bridge against Distance from centre f(x) = 0.17x + 60.11 f(x) = 0.1x + 60.92

Measured Linear (Measured) Theoretical Linear (Theoretical)

Figure 15: Graph of vortex profile for the 1st trial

Height from top of measuring gauge to bridge against Distance from centre f(x) = 0.15x + 75.2 f(x) = 0.08x + 76.07 Measured Linear (Measured) Theoretical Linear (Theoretical)

Figure 16: Graph of vortex profile for the 2nd trial

Height from top of measuring gauge to bridge against Distance from centre f(x) = 0.16x + 90.04 f(x) = 0.09x + 90.96 Measured Linear (Measured) Theoretical Linear (Theoretical)

Figure 17: Graph of vortex profile for the 3rd trial

7.0 SAMPLE CALCULATIONS Part A: Free Vortex Orifice diameter = 24 mm Distance from bridge to water surface, a = 225 mm At D = 72 mm and h = 82 mm, Pressurehead , X =330−a−h=330−225−82=23 mm 0.5

√

Velocity , V =( 2 gH ) = 2× 9. .81

m 1000 mm mm × ×10 mm=442.94 2 m s s

1 1 1 1 = 2= =7.72× 10−4 2 r 36 1296 mm2

From the graph of pressure head against 1/r2, Gradient ,

X =9 mm3 1 2 r

2

Substitute into equation

X K = , 1 2g r2

K2 =9 mm 3 2g

√

∴ K = 9.0 mm3 ×2 ×9.81

√

m 1000 mm mm4 mm2 × = 176580 =420.21 2 s m s s s

At D = 72 mm, r = 36 mm:

Theoretical velocity ,V =

K = r

mm2 s m =11.67 36 mm s

420.21

Part B: Forced Vortex Using the data from 1st trial: Angular velocity=2 π ×

No. of revolution 33 =2 π × =3.46 rad / s 60 s 60 s

Height from top of measuring gauge to bridge: h=h0 +

ω2 2 3.462 r =63+ 302=63.55 mm 2g 2(9.81 ×1000)

h=h0 +

ω 2 3.46 r =67+ 702=69.99mm 2g 2(9.81 ×1000)

h=h0 +

ω2 2 3.462 r =73+ 1102=80.38 mm 2g 2(9.81 ×1000)

2

2

8.0 DISCUSSION The experiment was conducted to determine the relationship between the velocity and angular velocity for free vortex and forced vortex respectively, with the vortex surface profile. The fluid mass for the free vortex rotates without external force; only through internal action or some rotation previously imported to it .On the other hand, forced vortex rotates by a constant torque exerted by some external source onto the fluid mass [8].

For the first part of the experiment, orifices with different diameters were used to observe and study free vortex. All the orifices show common trends whereby the velocity decreases as the radius increases. This causes a drop in elevation since pressure is the same on the free surface, and this H is constant [8]. This is proven in Table 1, 3, 5, and 7 whereby each orifice displayed this property. Comparison between different orifices also shows that bigger orifice diameter will yield greater vortex. Figure 1, 3, 5, and 7 also shows that the gradient for pressure head against 1/r2 is almost constant for each orifice diameter. Then, there is the profile between velocity and radius. The actual velocity is supposed to be constant just as the theoretical one, but our data deviates greatly from it. This may be due to human errors when conducting the experiment. The product between velocity and radius is supposed to be constant due to the axial vorticity component is zero [9]. The second part of the experiment involves the use of paddle at the bottom of the tank to create forced vortex. Figure 9, 10, and 11 shows that the value of slope for the measured data deviates slightly from the theoretical value. The measured slope for the 1st, 2nd, and 3rd trial is 0.169, 0.1512, and 0.1626 respectively while the theoretical slope is 0.1015, 0.0796, and 0.0865 respectively. The deviation is very small and we can conclude that the data is acceptable. The increase in angular velocity also shows the increase in height from top of measuring gauge to bridge, h. The slope of the curve increases as angular velocity increase due to the stream function formed in forced vortex is parabolic in nature [10].

9.0 CONCLUSION The objectives of this experiment were to determine the relationship between the velocity and angular velocity for free vortex and forced vortex respectively, with the vortex surface profile. From experiment 1, it can be concluded that as the radius of the orifice increases, the velocity decreases and bigger orifice diameter will yield greater vortex. However, the product between velocity and radius is not constant as it supposed to be due to human error. As for experiment 2, as the angular velocity increase the height from top of measuring gauge to bridge, h also increase. The slope of the curve increases as angular velocity increase due to the stream function formed in forced vortex is parabolic in nature. To sum it all, the objectives were achieved eventhough the data obtained is slightly different with the theoretical value.

10.0

RECOMMENDATIONS

1. Make sure that the flow and level of water is stable when the measurement is taken to ensure that the data obtained is accurate. 2. It would be better if there is and additional equipment given in order to have a better sight on flow visualization. 3. Make sure to locate the centerline of the flow field accurately. 4. In order to have more accurate results, the available range of diameter of orifices should be expanded.

11.0 REFERENCES 1.

Forced

vortex.

(n.d.).

Retrieved April 5,

2015,

from

https://www.physicsforums.com/threads/forced-vortex.430507/ 2.

Free and forced vortex - Chemical engineering other topics - Eng-Tips. (n.d.). Retrieved April 5, 2015, from http://www.eng-tips.com/viewthread.cfm?qid=126928

3.

JSME FED:Activity:Enjoy Fluid Experiments Lab.:Free Vortex and Forced Vortex. (n.d.).

Retrieved April 6,

2015,

from

http://www.jsme-fed.org/experiment-

e/2011_2/003.html 4.

Pattison, M. J. (n.d.). Fundamentals - Vorticess. Retrieved April 6, 2015, from http://www.thermopedia.com/content/1248/?tid=104&sn=1159

5.

Theory of a Vortex - Explore with Fouzan. (n.d.). Retrieved April 5, 2015, from http://fouzan.weebly.com/theory-of-a-vortex.html

6.

Vortex - Wikipedia, the free encyclopedia. (n.d.). Retrieved April 6, 2015, from http://en.m.wikipedia.org/wiki/Vortex

7.

What is FREE VORTEX FLOW? definition of FREE VORTEX FLOW (Science Dictionary). (n.d.). Retrieved April 6, 2015, from http://thesciencedictionary.org/freevortex-flow/

8. 9.

Singh, S. (2012). Experiments in Fluid Mechanics: PHI Learning. Dixon, S.L. (2005). Fluid Mechanics and Thermodynamics of Turbomachinery: Elsevier

Science. 10. Sinha, P., Sarkar, K., Pandey, B. K., & Nandi, N. On a few Aspects of Vortex Motion. 12.0

APPENDICES