NONLINEAR HYDRODYNAMIC FORCES

MANUFACTURE AND TRANSDUCER SELECTION

By Sachindra Max

2010

Overview of the Project

• This experiment is to

understand the fluid

hydrodynamic forces acting

on a floating body.

• This is practically applicable

for borehole oil drilling in

offshore and onshore.

• Properties of Fluids inside

the bore will be able to

measure from this equipment.

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Overview of the Project

• My main objective was to manufacture the experiment rig and select transducers to it.

• Apart form that I compared the experimental results in different conditions with a theoretically obtained values.

• Methods of multiple scale analysis is used to evaluate the theoretical values.

Experimental Results

Theoretical Values

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About bore hole drilling

• Bore holes may construct for may different purposes.

• In the Oil and Gas industry bore hole drilling is very important.

• Drilling is divided mainly in to 2 categories.

1. Onshore Drilling 2. Offshore Drilling

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About bore hole Drilling cont..

• This technology has a history of hundreds years.

• Drilling methods have been developed over the time for different purposes and environments to increase its efficiency.

• Few main drilling types,

I. Auger drilling

II. Air core drilling

III. Cable tool drilling

IV. Diamond core drilling

V. Hydraulic-rotary drilling

VI. Sonic (vibratory) drilling / Resonance enhanced drilling 5

Manufacturing of apparatus

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Experimental rig – Manufacturing

• The rig is adjusted couple of times to achieve the desired experimental results.

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Transducer Selection

Transducer Selection – Linear variable displacement transducer

• Linear variable displacement transducer (LVDT) is used to measure the amplitude of the oscillation.

• Change in position vertically of the actuator rod measures the amplitude of the oscillation.

• This device uses the eddy current principle to get the measurement.

• Accuracy of the LVDT used is sufficient enough for the experiment.

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Transducer Selection – Accelerometer

• Acceleration of the inner cylinder is measured by using this

device.

• Device is connected to a oscilloscope or to a computer software to get the experimental results.

• Fixing this unit to the experimental rig is easy and accuracy is high enough for the experiment.

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Transducer Selection – Pressure Transducer

• Pressure transducer is necessary to fix to the bottom of the large cylinder to measure the variable fluid pressure due to the impact of the actuator.

• This can be connected to a oscilloscope or to a computer software just like the Accelerometer or LVDT.

• Similarly fluid level can be measured by using the basic hydrostatic pressure equation.

P = hρg

• Suitable transducer for this experiment has a pressure range of 0 – 6 bar

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Transducer Selection – Vibro impactor

• This device creates the vertical sinusoidal force to vibrate the system.

• The metal bar is placed in a solenoid which creates a magnetic flux according to the current supplied.

• This is a very simple design and it’s the most appropriate for the experiment.

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Transducer Selection – Motor selection

• Initially experiment rig was supposed to design with a electric motor instead of a vibro impactor.

• Setup of the motor could be done as shown above.

• Main disadvantage of connecting a motor to the experiment is that it can create vibration NOT only vertically but also horizontally.

• Therefore it can create unnecessary friction to the vibrating system.

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Arrangement of the experimental rig

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Experimental rig – Signal generation / inputs

• A Sinusoidal current is generated from a signal generator and sent it to the vibro impactor, solenoid of the impactor creates a sinusoidal magnetic flux in the same frequency as the current. Therefore the metal bar will vibrates at the same frequency as the current.

• Amplitude of the sinusoidal motion of the metal bar is varied by varying the supplied voltage from the transformer.

• Best results of the experiment can be achieved by setting the vibrating frequency to 6Hz and voltage to 12v.

Transformer Signal

Generator Vibrating system

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Experimental rig – Results / data outputs

• Output signals from all the transducers are connected either to a oscilloscope or to a computer.

• Graphical representation of the data can be filtered well only in the computer software.

• Oscilloscope used to show the general idea of the motion graphically.

• Experimental data is taken at different conditions such as with water and without.

• Data is recorded as a function of time from the computer software and then plotted as shown in next slides.

Vibrating system

Transducers Oscilloscope / Computer

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Data acquisition for various cycles

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Water damped system with the LVDT : Displacement Vs. Time

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Water damped system with the Accelerometer : Acceleration Vs. Time

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Mathematical model for the experimental results

• Experiment rig can be simplified to a simple spring damper system as shown above.

• Springs of the rig will act same and water of the system behave as a damper.

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Transient motion of the system without water

• Suspended system is lifted up n released manually with a magnetic system and let the system vibrate freely with no external forced applied.

• Equation of the acceleration Vs. time graph of the system can assumed as;

1

• Oscillating Velocity of the system can be obtained by integrating the equation 1

2

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• Graphical representation of the equation 2

Velocity Vs. time – without water

( in a time interval of 0 – 2 seconds ) 22

• Equation 2 can be integrated once and obtained the displacement Vs. time equation

3

Displacement Vs. time – without water

( In a time interval of 0 – 2 seconds) 23

Theoretical model for the system

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Method of multiple scales

• This is a perturbation method.

• Duffing equation is used to evaluate the theoretical values.

• This equation can be used to this experiment since it’s amplitude is low and it can be used for water damping systems.

• Duffing equation :-

• This equation does not contain a damping term. There for its modified with an additional damping term.

• Duffing equation with damping term :-

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Duffing equation • Substitutions;

• After the substitution coefficients of each power of ϵ is separated;

• Solutions for u0 , u1 , u2 obtained.

• u is obtained by substituting u0 , u1 , u2

• Where;

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Comparison

• Data obtained experimentally and numerically needs to compared.

• Amplitude of the oscillation will be lower in experiment values due to the friction acting at contacting points.

• The values can be compared as shown in the next slide.

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Graphical comparison

Experimental results Theoretical values 28

Conclusion

• Properties of water such as the damping term can be evaluated by comparing the two methods.

• Accuracy of the system can be increased buy remanufacturing some parts. And by using proper rigid connections.

• Experiment rig needs to be modified further for real life applications.

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Thank you. Any Questions ?

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