my report

EXPERIMENTAL STUDY OF WAVE PROPOGATION IN A STRATIFIED MEDIUM

A Report of the work done under the Summer Research Fellowship Programme - 2011

Submitted by:

Harsha NU.G. student

Department of Chemical EngineeringNational Institute of Technology Karnataka

Surathkal– 575025

Supervised by:

Dr.K.R.Sreenivas Professor

Engineering Mechanics UnitJawaharlal Nehru Centre for Advanced Scientific Research

Jakkur, Bangalore – 560 064

Acknowledgements

I would like to thank Prof. K.R.Sreenivas for providing me the opportunity to

work on this research project and very grateful for his constant guidance and

support in the experiments. In addition, I would like to express my gratitude to

labmates – Siddarth A V, Srikanth D M, Siddharth and Dhiraj for their advice,

cooperation and help in the lab during experiments and analysis. Finally, I

would like to thank my family members who have given me moral support and

encouragement throughout.

CONTENTS

Page No.

1. Introduction 3

2. Experimental setup 4

2.1 Stepper motor 7

3. HP 54615B oscilloscope 9

3.1 Labview VI for HP 54615B 11

3.2 MATLAB program for HP 54615B 12

4. SCB-68 14

4.1 LABVIEW VI for SCB-68 16

4.2 MATLAB program for SCB-68

4.3 Photodiode and connections to SCB-68

17

5 Results 19

6 Conclusions and future scope 25

1.0 Introduction

Stratification of ocean water is a naturally occurring phenomenon that is important to the structure, circulation and productivity of the oceans. The formation of vertical stratification in the water column is a consequence of water masses with different densities. Water density is strongly influenced by temperature and salinity; with less dense, warmer surface waters floating on top of denser, colder waters. The boundary between the warmer and cold waters is called the thermocline.

The phenomenon of gravity wave occurs when a fluid element is displaced near the interface of two mediums or in a region with varying density. Gravity waves on an air-fluid interface are called surface gravity waves and if the interface separates fluids with slightly different densities, then a much slower version of surface waves, internal gravity waves occur. So, internal waves are gravity waves that oscillate within, rather than on the surface of, a fluid medium.

There have been a large number of studies devoted to the understanding of generation, propagations and mechanics of these internal gravity waves. They play an important role in marine engineering, since the drag generated in density stratified medium is significantly different from a uniform density medium [2].

When a fluid element is displaced on an interface or internally to a region with a different density, gravity tries to restore the parcel toward equilibrium resulting in an oscillation about the equilibrium state. The parcel oscillates about its equilibrium position at a natural frequency determined by the local density stratification and the fluid’s compressibility. This frequency is called the Brunt-Väisälä frequency. This is used to characterize the degree of stratification in the ocean.

where ρ, the potential density, depends on both temperature and salinity.

The aim of the current experiment is to simulate ocean conditions and study these internal gravity waves produced in a density stratified fluid when it is disturbed with a propeller. The information about these gravity waves produced by the propeller is obtained by knowing the changes in refractive index at a

point because of the density perturbations. This change in refractive index can be captured using a laser and a photodiode arrangement. The velocity of the waves will have to be calculated by finding the time lag obtained in the two probes kept at a known distance. The data obtained will have to be characterized to know the information about the propeller such as rotational velocity, diameter and so on. This finds application in naval sectors where it can be used to obtain information about ships and submarines by knowing their gravity wave signatures.

2.0 Experimental Setup

The initial experiments are done in a smaller scaled down tank to get a rough idea about the behavior of the waves and to test the circuits and the data logging units before shifting to the main 3000mm x 750mm x750mm tow tank.The experimental setup consists of a large glass tank fitted with a DC motor which is carefully insulated from water. A quarter-circular plexi-glass sheet fitted with baffles and with a hole in the center is used as a diffuser, to cut off the vertical velocities of the fluid, so that the layers of different densities pile upon without mixing taking place as shown in Fig 2.1. Saline water of varying concentration of salt is prepared and added layer-wise. This is allowed to settle for a day to ensure continuous density variation.When light is passed through a density stratified medium it undergoes refraction and a phase change and due to the continuously varying index of refraction, the amount of bending is different from that of a homogenous medium.Two duo-lateral photosensitive diodes (duma optronics) are used to sense the refracted light waves which are generated from a 5mW, Class 3R (Coherent) laser source, emitting red light. Duo-lateral photodiodes provide a continuous analog output proportional to the displacement of the centroid of a light spot from the center, on the active area of the diode.

Fig 2.1 Front view of the experimental setup with lasers and photodiodes in positionThe wave propagation is first observed by BOS (Background Oriented Schlieren) technique. A translucent sheet having black lines is fixed on one side of the tank depending on the plane to be visualised. This sheet is illuminated by halogen lamps which are placed behind it. The camera placed in front of this captures the flow in the background of the sheet.

The photodiodes are connected to NI SCB-68 signal conditioning box and then to a NI-PCI card for data acquisition using labVIEW software. The initial experiments are done in a smaller scaled down tank to get a rough idea about the behavior of the waves and to test the circuits and the data logging units. Experiments are performed in the big tank with motor fixed at one face and the first laser-probe pair at a distance of 25 cm and the second laser-probe pair at varying distances. Data acquisition was tried using Agilent 34902A datalogger, HP 54615B and then NI SCB 68.

Fig 2.2: data acquisition circuit 2.1 Stepper Motor Stepper motor provides a better control of rotational speed of the shaft when compared to DC motors. Hence a 5V stepper motor was used to create a disturbance. Stepper motor was connected to a stepper motor controller circuit, L293D, which receives signals from a customized board having ATMEGA-8 microcontroller (Fig 2.2). The microcontroller was programmed using USBASP AVR programmer, the code was basically written in C programming style.

Fig 2.3 From left: Stepper motor Controller, ATMEGA-8 microcontroller

Below: AVR programmer

Since the motor has to be placed in a stratified fluid medium it has to be properly insulated exposing only the propeller and the shaft. The simplest way of achieving this was by cutting the opening of the balloon so that the motor can be inserted in it and making a small hole for the shaft to protrude out. This hole was further insulated using Teflon tapes and the connecting wires by insulating tapes (Fig 2.3).

Fig 2.4 Stepper motor fitted with propeller and well insulated from water

The following program was used to control the speed of the stepper motor. The code was written in Atmel AVR Studio and the hex file was generated, which was burnt to the microcontroller using the Progisp software. The speed of the motor was varied by changing the value of the delay time in the program appropriately.#include<avr/io.h>#define F_CPU 1000000UL#include<stdio.h>#include<util/delay.h>main(){

DDRD=0xFF;while(1){

PORTD=0x01;_delay_ms(25);PORTD=0x04;_delay_ms(25);PORTD=0x02;_delay_ms(25);PORTD=0x08;_delay_ms(25);

} }

3.0 HP 54615B OscilloscopeOscilloscopes serve as an excellent tool for visualizing the signals from sensors and can also be used for data acquisition depending on the model. HP 54615B digital oscilloscope having capacity of collecting data at 1GSa/ sec at 500MHz was used to capture the signals [9]. The oscilloscope has 2 channels and hence the sensitivity of the probes is first examined and then the one with maximum sensitivity from each probe is connected to a channel. The sampling, volts per division and the time scale is adjusted appropriately by giving small disturbances and observing the output.One of the major challenges in data acquisition is noise reduction from the circuits, connecting wires and the power lines. The oscilloscope has an in built

filter which can be used to reduce the noise from power lines, corresponding to 50 Hz. The circuit is sandwiched between sponges and then covered with aluminium foils which are then grounded. This shields the signals from capturing the stray radiation from the surroundings. Since HP 54615B has a storage module and supports RS-232 connection, the data obtained can be stored in computers and later processed. Agilent IO control software has to be installed for the detection of the oscilloscope. Due to lack of appropriate softwares to read data from this oscilloscope, a program has to be written in MATLAB for serial communication and sending and receiving ASCII data. Alternatively LABVIEW provides drivers which can detect the oscilloscope and thus a VI (Virtual Instrument) can be created and the waveforms can be easily obtained. The various commands for programming can be obtained from the ‘Agilent 54600 programmer’s guide’. The major disadvantage of using an oscilloscope for data acquisition is that the acquisition is not continuous. The ‘:WAV:DATA?’ query is used to get the waveform data and the number of points it can transmit is limited to 2000. This query is preceded by set of commands for digitizing the channel and hence even if the process is looped there is a certain delay in capturing the data and hence a part of signal is lost which is undesirable considering the magnitude of time delay.

3.1 LABVIEW VI for OscilloscopeThe drivers for the oscilloscope have to be installed before running the VI and the commands in each ‘write block’ of different functions blocks provided by the drivers are suitably modified to write the command which can be understood by the oscilloscope (Fig 3.1). These commands are again obtained from the programmer’s guide.

Fig 3.1 Front panel of the VI for HP 54615B oscilloscope and the block diagram showing

data flow

3.2 MATLAB program for OscilloscopeThe following program is written in a m-file and run to initialize the serial connection, get the waveform data, and plot them on a graph [8].%Initialisation of variablesk = 0;A=zeros(0,1); % Instrument Settings% Setting up the portvisaObj = visa('agilent','ASRL3::INSTR');% Set the buffer sizevisaObj.InputBufferSize = 100000;% Set the timeout valuevisaObj.Timeout = 1000;%Set the flow controlvisaObj.Flowcontrol = 'Hardware';% Set the Byte order% Open the connectionfopen(visaObj); % Instrument control fprintf(visaObj,':STOP');% Specify data from Channel 1fprintf(visaObj,':WAVEFORM:SOURCE CHAN1'); % Set timebase to mainfprintf(visaObj,':TIMEBASE:MODE MAIN'); while k<=4% Set up acquisition type and count. fprintf(visaObj,':ACQUIRE:TYPE NORMAL');fprintf(visaObj,':ACQUIRE:COUNT 1');% Specify 5000 points at a time by :WAV:DATA?fprintf(visaObj,':WAV:POINTS:MODE RAW');fprintf(visaObj,':WAV:POINTS 1000');%Continuous acquisition % Now tell the instrument to digitize channel1fprintf(visaObj,':DIGITIZE CHAN1');% Wait till completeoperationComplete = str2double(query(visaObj,'*OPC?'));while ~operationComplete operationComplete = str2double(query(visaObj,'*OPC?'));end% Get the data back as a WORD (i.e., INT16), other options are ASCII and BYTEfprintf(visaObj,':WAVEFORM:FORMAT WORD');% Set the byte order on the instrument as wellfprintf(visaObj,':WAVEFORM:BYTEORDER LSBFirst');% Get the preamble block

preambleBlock = query(visaObj,':WAVEFORM:PREAMBLE?');% The preamble block contains all of the current WAVEFORM settings.

% Commmand to read datafprintf(visaObj,':WAV:DATA?');waveform.RawData = binblockread(visaObj,'uint16'); fread(visaObj,1); % split the preambleBlock into individual pieces of infopreambleBlock = regexp(preambleBlock,',','split'); A = vertcat(waveform.RawData ,A); k=k+1;end

%Run the front displayfprintf(visaObj,':RUN');% Close connection.fclose(visaObj); % Data processingwaveform.RawData = A;% Maximum value storable in a INT16maxVal = 2^16; % store all this information into a waveform structurewaveform.Format = str2double(preambleBlock{1}); waveform.Type = str2double(preambleBlock{2});waveform.Points = str2double(preambleBlock{3});waveform.Count = str2double(preambleBlock{4}); % Keep this always 1waveform.XIncrement = str2double(preambleBlock{5}); waveform.XOrigin = str2double(preambleBlock{6}); waveform.XReference = str2double(preambleBlock{7});waveform.YIncrement = str2double(preambleBlock{8}); waveform.YOrigin = str2double(preambleBlock{9});waveform.YReference = str2double(preambleBlock{10});waveform.VoltsPerDiv = (maxVal * waveform.YIncrement / 8); waveform.Offset = ((maxVal/2 - waveform.YReference) * waveform.YIncrement + waveform.YOrigin); waveform.SecPerDiv = waveform.Points * waveform.XIncrement/10; waveform.Delay = ((waveform.Points/2 - waveform.XReference) * waveform.XIncrement + waveform.XOrigin);

% Generate X & Y Datawaveform.XData = (waveform.XIncrement.*(1:length(waveform.RawData))) - waveform.XIncrement;waveform.YData = (waveform.YIncrement.*(waveform.RawData - waveform.YReference)) + waveform.YOrigin;

% Plot itplot(waveform.XData,waveform.YData);set(gca,'XTick',(min(waveform.XData):waveform.SecPerDiv:max(waveform.XData)))xlabel('Time (s)');ylabel('Volts (V)');title('Oscilloscope Data');grid on; % Delete objects and clear them.delete(visaObj); clear visaObj;

4.0 SCB-68 Board and NI 6024E

The SCB-68 is a shielded I/O connector block with 68 screw terminals which is used for capturing signal from the photodiode and it can be connected to a National Instruments 68-pin or 100-pin DAQ device, like NI 6024E [5]. The SCB-68 consists of a general breadboard area for custom circuitry and sockets for interchanging electrical components (Fig 4.1). These sockets or component pads allow filtering, 4 to 20 mA current input measurement, open thermocouple detection, and voltage attenuation. A floating signal source is the one which is not connected to the building ground system and so the photodiodes can be classified as floating signals [6]. Such signals are connected to the SCB board through differential channels (Fig 4.2). Differential signal connections reduce noise pickup and increase common-mode noise rejection.

Each photodiode has 4 voltage outputs and hence 8 channels are required to get all the information from the photodiodes. This is easily accomplished since SCB-68 has 8 differential inputs on the board.

Fig 4.2 SCB-68 printed circuit board diagram

The photodiode sensor can be read by reading the voltage measurements using AI 0 and AI 8 in differential mode. For a scale from 500mV to -500mV the accuracy is about 0.195mV. More details on this can be obtained from the ‘NI 6023E/6024E/6025E Family specifications’ manual [7]. The data is simultaneously obtained in the front panel of the Data Acquisition VI and is stored in a text file.

4.1 LABVIEW VI for SCB-68

The signals from the SCB-68 board are received by the computer through NI 6024E DAQ card. Thus a virtual instrument is created in LABVIEW with a front panel as shown in the Fig 4.3. All the eight channels are monitored and simultaneously the data is also written to a text file in ‘.lvm’ format (Fig 4.4).

Fig 4.3 Front panel of the VI for data acquisition

The DAQmX driver has to be installed so that the DAQ card is detected and updated so that it is compatible with the LABVIEW version present in the computer.

Fig 4.4 Block diagram showing the data flow

MATLAB Program for SCB-68

The data obtained from the VI in ‘.lvm’ format is read using a simple MATLAB program and the plotted.

clear allclose allclc % Read the excel file generated by LABVIEWv1=xlsread('result_data2JUly7.xlsx','C1:C180000');v2=xlsread('result_data2JUly7.xlsx','G1:G180000'); % Offset two probes to distinct them for better visualizationv2=v2-0.05; %Plot the dataplot(v1)hold onplot(v2,'r')Xlabel('Time'), Ylabel('Voltage'); title('Variation of voltage signals of the Photodiodes with time');hold off

The photo diode

This is a Spot On Lateral Effect 10x10 mm PnP detector. The pin diagram is depicted in the following picture.

Pins 2, 3, 4, 9 of each photodiode are connected to AI 0(68), AI 1(33), AI 2(65), AI 3(30) and AI 4(28), AI 5(60), AI 6(25), AI 7 (57).

5.0 Results:

Experiments were conducted in the small tank

Stratification levels: 1000-1050 gm/cm3 in steps of 10 gm/cm3 for 2 cm and

having a 10cm layer on 1000 and 1050 gm/cm3.

Type of motor used: DC motor

Voltage of input power supply to motor: 3.5V

Distance between probes: 26cm

Fig 5.1 Variation of voltage output from Photodiodes with time

From the graph of variation of voltage signals from the photodiodes it can be

see that there is a certain time delay between two probes catching the signals.

When the motor is started, the voltage output in the first probe, being closer to

the propeller, fluctuates because of the variation in refractive index. The second

probe fluctuates after a certain time as seen from Fig 5.1. From image

processing toolbox of MATLAB, by calculating the number of pixels between

the two points and then scaling it, it is seen that this time delay is about 10s.

Experiments in the large tankSeveral experiments were conducted in the large tank by varying parameters like distance between the probes, height of the second probe, and angle of the motor.Stratification levels:

1000-1050 kg/m3 in steps of 10 kg/m3 for 2 cm, having a 10cm layer on 1000

and 20cm of 1060 kg/m3.

Type of motor used: DC motor

The first laser and photodiode arrangement was fixed at a distance of 25cm from the motor and at the same height as that of the motor. Position of the second laser- photodiode arrangement was varied as 0.5m, 1m, 1.5m, and 2.0m from the first probe in each trial.

Experiment 1: Distance between the probes: 0.5mVoltage to the motor: 3.5VHeight of the first probe: 5.2cm from the top surface of waterHeight of the second probe: 4.6cm from the top surface of waterTime delay: 6.89sLinear Velocity: 7.25cm/s

Experiment 2: Distance between the probes: 1mVoltage to the motor: 3.5mHeight of the first probe: 5.2cm from the top surface of waterHeight of the second probe: 4.6cm from the top surface of waterTime delay: 16.29sLinear Velocity: 6.14cm/s

Experiment 3: Distance between the probes: 0.5m tiltedVoltage to the motor: 3.5mHeight of the first probe: 6cm from the top surface of waterHeight of the second probe: 4.6cm from the top surface of waterTime delay:32.79 Linear Velocity: 1.52cm/s

Experiment 4: Distance between the probes: 1.5mVoltage to the motor: 3.5mHeight of the first probe: 15cm from the top surface of waterHeight of the second probe: 15cm from the top surface of waterTime delay: 24.076sLinear Velocity: 6.23cm/s

Conclusion:It was observed that the internal waves due to the propeller motion converge and diverge in certain regions and therefore the height of the probes had a profound effect on the time delay observed. Also, the angle of the motor influenced the linear velocity to a great extent.The rpm of the motor, the distance between the probes, stratification levels influence the velocity as well.This clearly indicates that flow visualisation is very important to know the nature of internal waves developed. Also, it was noted that there was a finite time delay between probes every time.

Future scope:Further experiments can be conducted for varying stratification levels, different propellers, different motor speeds.Flow visualisation for a particular stratified medium and a specific motor-propeller combination can be done and the nature of the internal waves developed i.e. the converging and diverging regions can be found.Later, experiments can be carried out for varying heights of the photodiodes appropriately. Also, experiments with different angles of the motor can be done as well.It is very important to know the velocity of the disturbance for varying hydrostatic head. This is of extreme importance in the naval sector.

6.0 References

1. Wake flow measurements in towing tanks with piv, J. Tukker, JJ. Blok, G. Kuiper, R.H.M

Huijsmans, 9th International Symposium on Flow visualization, 2000

2. On wakes in stratified fluids, G.S Janowitz, Journal of Fluid Mechanics, 1968

3. Stratified propelled waves, Patrice Meunier, Geoffrey R Spredding, Journal of Fluid

Mechanics, 2006

4. An easy method for measuring surface wave signals, Matti Nummelin, Ann Zool Fennici 19:

237-238, 1982.

5. DAQ: SCB-68 User Manual for Advanced Functions, National Instruments

6. SCB-68 User Guide, National Instruments

7. NI 6023E/6024E/6025E Family Specifications, National Instruments

8. Programmer’s Guide – Agilent 54600 series Oscilloscopes, Agilent Technologies

9. HP BenchLink XL 54600, ActiveXTM Control and Automation Server Programmer’s

Reference, Agilent technologies

10. Photodiode Characteristics, UDT Technologies

11. Fundamentals of signal analysis, Application Note 243, Agilent Technologies