Assign03 Venturimeter

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STAFFORDSHIRE UNIVERSITY

Assignment 3:

Fluid Flow and Pressure Distribution in

Venturi Meter

Submitted by: Mohamed Humaid Al-Badri (09032170)

Email: [email protected]

Award Title: Mechanical Engineering

Module Title: Applied Structural Integrity

Module Code: CE00449-7

Submitted to: Prof. Peter Ogrodnik

Submission Date: 14/01/2012

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Abstract

The pressure distribution along the wall of Venturi tube widely used in

many industry tests and applications. Here we did an experiment on the

wall of the venturi meter to check the internal distributed pressures.

Then, analyse the experimental data and plot graphs for it. Also, study

the theory of the venturi meter and calculate the data theoretically by

using Bernoulli’s equation. The concentration here is to analyse the

venturi meter internal pressures by Ansys CFX, which explores the use of

solid works to analyse the fluid flow in the tube. At the end of the report,

there is a compression between these analysis methods. The comparison

shows that the Ansys CFX model results not matching the other two

results due to some assumption made in this model.

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Table of Contents:

Table of Contents: ......................................................................................................................................... 3

List of Figures: ............................................................................................................................................... 4

List of Tables: ................................................................................................................................................ 4

1. Introduction: ............................................................................................................................................. 5

2. Experiment: ............................................................................................................................................... 6

2.1 Description and Apparatus: ................................................................................................................ 6

2.2 Procedure: ........................................................................................................................................... 7

3. Theory of the Experiment: ........................................................................................................................ 8

4. Ansys of the Experiment: .......................................................................................................................... 9

4.1 Mesh Refinement:............................................................................................................................. 10

5. Results: .................................................................................................................................................... 11

5.1 Experimental Results: ....................................................................................................................... 11

5.2 Theoretical Results: ........................................................................................................................... 12

5.3 Ansys Results: .................................................................................................................................... 13

6. Comparison of Results: ........................................................................................................................... 14

7. Conclusion: .............................................................................................................................................. 16

8. References: ............................................................................................................................................. 17

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List of Figures:

Figure 1 Venturi tube .................................................................................................................................... 5

Figure 2 Experiment Venturi meter .............................................................................................................. 6

Figure 3 Locations of pressure tapings ......................................................................................................... 7

Figure 4 Ansys model for venturi meter ....................................................................................................... 9

Figure 5 Comparison for the convergence in CFX ....................................................................................... 10

Figure 6 Mesh refinements for venturi meter ............................................................................................ 10

Figure 7 Mesh refinements before and after ............................................................................................. 11

Figure 8 Comparison of experimental pressure and velocity ..................................................................... 12

Figure 9 Comparison of theoretical pressure and velocity ......................................................................... 13

Figure 10 The velocity for Runs 1 and 2 ...................................................................................................... 14

Figure 11 The pressure for Runs 1 and 2 .................................................................................................... 14

Figure 12 Comparison graphs between Experimental, Theoretical and Ansys .......................................... 15

List of Tables:

Table 1 Experimental Result for Run 1 ........................................................................................................ 11

Table 2 Theoretical Results ......................................................................................................................... 12

Table 3 Comparison results between Experimental, Theoretical and Ansys .............................................. 15

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1. Introduction:

The Venturi tube is used to determine flow rate through a pipe. Differential pressure is the

pressure difference between the pressure measured at D (venturi inlet) and at d (neck) as

shown in Figure 1 [1]. Normally, the venturi tube has less head loss than nozzles and orifices

due to its streamlined design [1]. The flow streamline in venturi meter is laminar when the

Reynolds number is in the range of 105 to 106.

Figure 1 Venturi tube

The main characteristics of the venturi meter, there is no restriction to the flow down the pipe,

and it can be manufactured to fit any required pipe size. Also, the temperature and pressure

inside the tube does not affect the meter or its accuracy.

In this experiment, we will calculate the pressure distributed inside the tube using the data

from experiment. Also, calculate the pressure theoretically using Bernoulli’s equation.

Moreover, analyse the internal pressure by using Ansys which is effectively there are three

stresses (pressure) radial, hoop and longitudinal. But here the Ansys analysis will be on the

radial stresses (normal stresses) which we can compare them with experimental and theoretical

results.

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2. Experiment:

The flow rate is supplied through the venturi tube and after the steady stat flow is achieved the

flow rate is measured by using a flow-meter, and the pressure readings measured by piezo-

meter.

2.1 Description and Apparatus:

The experiment apparatus consist of flow bench, weighing tank, lever arm, hydraulic bench,

trip valve, inner tank, pump, manometers, thermometer, stop watch, flow-meter and piezo-

meter. The water come from hydraulic bench and enters the venturi meter, which flows into a

rapidly diverging section, flowed by neck section, then flows into a long diffuser. This change of

cross-section of the venturi tube gives different values of flow along the tube. After that, the

flow returns via a control valve to the hydraulic bench where the flow rate can be measured by

using catch-tank and the stop watch. The venturi meter has 11 test positions (A – L) as shown in

Figure 2.

Figure 2 Experiment Venturi meter

Also the location of each manometer pressure taps can be taking from the Figure 3, which

these measurements will help in modeling the venturi meter in Ansys.

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Figure 3 Locations of pressure tapings

2.2 Procedure:

The procedure of the experiment as follows [2]:

1. First of all, we made sure that, the air purge valve on the upper manifold is tightly

closed.

2. Then, we kept the apparatus flow control and bench supply valve to approximately 1/3

their fully open positions.

3. Then, Switching on bench supply valve and allow water to flow, at the same time, we

taped manometer tubes in order to remove air bubbles from apparatus.

4. Then, closing apparatus flow control valve.

5. Then, releasing air purge valve to allow water to raise approximately 2/3 the way up the

manometer tubes.

6. After that, opening apparatus flow control valve to obtain full flow.

7. Finally, repeating the above and make 3 runs, and taking all readings for every turn.

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3. Theory of the Experiment:

According to Bernoulli’s equation, the ideal pressure distribution can be given as [2]:

(1)

Where P is the pressure (Pa), g is the gravitational acceleration (9.81m/s2), is the fluid velocity

(m/s) and is the density of the fluid at local temperature (kg/m3) [2]. Using the above

equation for P1 and the velocity at each respected points as the reference, Bernoulli’s equation

can be written as [2]:

(2)

And it can be written for venturi meter as [2]:

(3)

Where Cd is the Coefficient of Discharge, and also the velocity can be obtained from the

following equation [2]:

(4)

Where n indicates the point of interest where the velocity and area of point n can be obtained

using equation (4). Also, the mass flow rate can be obtained from the following equation:

(5)

Where, the water physical properties are taken at temperature 25oC. Also, the pressure shown

on manometer can be obtained from equation:

(5)

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Where the h is the height of flow rate and it should be in meter. From equations (2) and (3) the

pressure and coefficient of distribution can be calculated. Then all these data and result will be

tabled in result section.

4. Ansys of the Experiment:

In Ansys, the venturi meter is modeled as per the dimensions shown in Table 1. The conditions

in this modeling are same of the conditions at experiment setup, and the testing conditions are

defined by the boundary conditions and they are shown in Figure 4.

Figure 4 Ansys model for venturi meter

The boundary conditions we applied here are the section A (V1 = 0.57 m/s) and the section L (P

= 2432.88 Pa). Also, the venturi meter walls are set as no slip, and then using CFX to solve.

During CFX analysis the result for the model is depending on the mesh refinement. The venturi

meter analysis here was done and performed for 100 and 1000 iterations as shown un Figure 5

below.

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Figure 5 Comparison for the convergence in CFX

4.1 Mesh Refinement:

The mesh refinement for the venturi meter is done in static structural in Ansys. After some

trials, we got the equivalent stress as shown in Figure 6 and 7 below.

Figure 6 Mesh refinements for venturi meter

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Figure 7 Mesh refinements before and after

It is observed that from the graph above is that, the maximum stress is at about 15000

elements. So, at this number of elements, we applied CFX to solve the Ansys model.

5. Results:

5.1 Experimental Results:

According to the venturi meter, we did calculation for the pressure using equation (5) at each

section, and the results are shown in Table 1 and Figure 8 below.

Table 1 Experimental Result for Run 1

Run 1

Meter reading (m^3)

start 94.06000

end 94.15000

Time (sec) 300.00000

Measured water flow (m^3 / sec)

0.00030

Measuring point water level (m) Area (m^2) Pressure (N/m^2) Velocity (m/s)

A 0.264 0.0005309 2589.84 0.57

B 0.262 0.0004227 2570.22 0.71

C 0.220 0.0002659 2158.20 1.13

D 0.154 0.0002011 1510.74 1.49

E 0.168 0.0002214 1648.08 1.36

F 0.200 0.0002679 1962.00 1.12

G 0.200 0.0003192 1962.00 0.94

H 0.232 0.0003746 2275.92 0.80

J 0.240 0.0004348 2354.40 0.69

K 0.246 0.0004992 2413.26 0.60

L 0.248 0.0005309 2432.88 0.57

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Figure 8 Comparison of experimental pressure and velocity

5.2 Theoretical Results:

Using the dimensions of the venturi meter and by using the equations explained in theoretical

sections, the results are shown in Table 2 below.

Table 2 Theoretical Results

The comparison between the velocity and pressure got it theoretically is shown in Figure 9.

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Figure 9 Comparison of theoretical pressure and velocity

5.3 Ansys Results:

After the mesh refinement, the CFX analysis was obtained for the venturi meter. The Ansys

results comparison for velocity and pressure for two runs (Run 1 and Run2) are as shown in

Figures 10 and 11.

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Figure 10 The velocity for Runs 1 and 2

Figure 11 The pressure for Runs 1 and 2

6. Comparison of Results:

According to the above, the pressure head readings of the experiment and theoretical results

are close to each other, but the Ansys model CFX is far away and not matching these results. All

these results are as shown in Table 3 and Figure 12 below.

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Table 3 Comparison results between Experimental, Theoretical and Ansys

Experimental Theoretical Ansys

2589.84 2589.84 2294.58

2570.22 2490.12 2286.35

2158.2 2074.13 2182.48

1510.74 1559.01 2014.74

1648.08 1769.58 2127.15

1962.00 2084.36 2198.01

1962.00 2284.83 2237.56

2275.92 2415.67 2376.54

2354.40 2505.07 2284.03

2413.26 2567.21

2432.88 2589.84

Figure 12 Comparison graphs between Experimental, Theoretical and Ansys

The big difference in results between Ansys model and the other two came because of

improper boundary conditions at walls in CFX analysis, which it was assumed there is no slip at

walls. Also, there is no calculation in the viscosity of the fluid inside the tube. In addition the

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mesh refinement for the venturi meter is done in static structural since this will consider the

walls of the venturi meter as solid, which is not true and from here it gives different readings.

7. Conclusion:

In view of the above, the results from Ansys CFX is not matching the other two results of

experimental and theoretical due to the assumptions we made and due to the mesh refinement

of the venturi meter which is done in static structural instead of CFX itself. We think that, the

Ansys CFX needs more improvement and more consideration in mesh refinement to get proper

results by considering the materials of the venturi meter and the liquid viscosity.

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8. References:

[1] Baker, R. C. (1996), An Introductory Guide to Industrial Flow, R. C. Baker Ed. Suffolk, London,

UK.

[2] Anderson, J. D., Degroote, J., Degrez, G., Erik, D., Grundmann, R., & Vierendeels, J. (2009),

Computational Fluid Dynamics, J. F. Wendt, Ed., Chaussee de Waterloo, Rhode-Saint-Genese,

Belgium.