Turbulent Flow and its Effect on Sediment Transport

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Chapter III Preparatory Work

Most experimental work is preceded by a large amount of preparations. This chapter discusses the development and alterations made to many aspects of these experiments and the equipment involved.

Electromagnet

A simple electromagnet is a coil of wire around a solid core. When electrical energy is applied to the coil, current flows through the coil creating an electromagnetic field with force flowing perpendicular to the current; cut the current off, the magnetic field collapses and the force dies. Electromagnets are easily made, however to produce significant levels of force, a commercially made electromagnet is needed.
The amount of force produced by an electromagnet is dependent on not only the amount of current, but also the physical properties of the magnet such as number of turns of wire, the core material and the distance the magnet is from the object it is attracting. (Electromagnetic force will be discussed further in the Analysis section). The amount of electromagnetic force decreases significantly with any size air gap between the magnet and the object it is attracting, which is why most electromagnets are sold as surface mount electromagnets and their force abilities are listed for that use. In addition, at the start of the preparation, it was not known what type of forces the researchers would be looking for in the resulting experiments. These two complications made selection of an appropriate electromagnet a trial and error situation.
The magnetic flux of an electromagnet is highly affected by the medium through which that flux must travel. As mentioned earlier, magnetic flux density decreases significantly while passing through air. Plonus (1978) gives the expression where B is the magnetic flux density in teslas, µ0 is the permeability of free space, N is the number of turns of wire, I is the current in amperes, and h is the air gap distance in centimeters. This expression describes how the flux density will significantly decrease as the face of the electromagnet is moved further from the object which it is trying to attract. During preliminary testing of electromagnets, it was found that surface electromagnets with capabilities less than the currently used 32 pull-lbs had difficulty moving the test particle from a distance of 1 cm.
Another aspect of the electromagnet to consider was the shape. It was felt that a circular faced electromagnet would allow for easier estimation of the center of the magnetic force. Also, to be able to try and point the electromagnetic force towards the center of the particle as best as possible, a large faced electromagnet would not work; higher pull-force rated electromagnets tend to have larger core diameters resulting in wider magnetic fields. The 1 inch diameter round electromagnet with ½ inch diameter iron core seemed to have the best characteristics for use in these experiments.

Signal Programming

The key to these experiments is controlling the force amplitude and duration (pulse) felt by the particle. To do this, a computerized pulse generation program was created that could send signals out through a data acquisition (DAQ) system and the pulse felt by the electromagnet read back into the program through the DAQ system.
The pulse generation program is user defined. The program is designed to take the inputs from the user for pulse parameters, such as amplitude and duration, and insert these parameters into an array. This array is then sent to the DAQ system at a user specified rate. The program will repeat until stopped by the user. The user can choose the pulse to repeat in a variety of different means: (1) repeat same pulse, (2) repeat with increasing amplitude and constant duration, (3) repeat with increasing duration and constant amplitude, (4) repeat with random values for duration and constant amplitude, (5) repeat with random values for amplitude and constant duration, (6) repeat with random values for both amplitude and duration. These experiments make use of program options (1), (2), and (3). The other options were designed with simulation of a random turbulent event in mind, although no experiments have been done using these options.
There are several limitations involved with the pulse generation program. Due to constraints from the DAQ system, the program is specified to run under software timing. There are two methods by which a program can run, hardware timed and software timed. Hardware timed programs are controlled by the clock within the DAQ system. The user may specify a particular sample rate and the pulses are generated in a highly accurate manner. Software timed programs are controlled by the timing of the software. This method cannot be used with a specified sample rate. The user may decide the length of the array (number of samples to send out) and the wait time between samples which can be used to calculate an average sample rate. However, because this type of program is run by the software clock, it is not as accurate as the hardware clock and can have faster or slower wait times depending on the computer and other programs running, etc. As mentioned earlier, it would be ideal to be able to adjust the pulses at the smallest rate possible to more accurately determine the pulse required for initial movement. The DAQ system used in the experiments however was limited to a 300 S/s analog output rate which correlates to a minimum pulse duration of 3ms. For example, an array of 400 points is created where 399 points have a value of 0 and 1 has a non-zero value. This is the pulse. The duration is one point, however the DAQ must wait 3 ms before sending out the next point, so that non-zero pulse will last for 3 ms before changed to a zero value. Adding another point to the non-zero pulse lengthens the pulse duration to 6ms before changing back to a zero value. Therefore, each pulse that is sent out increases by 3 ms interval; the true pulse duration needed to create initial movement however, could be less than the recorded pulse duration. For example, if the particle was not removed at 9 ms, but was removed at 12 ms, it is possible that a duration of 11, 10, even 9.5 ms would have been able to remove the particle. It is impossible to determine with this current system which duration is the minimum required to dislodge the particle. This determines the maximum error or uncertainty in these calculations.
One way to bypass this source of error was to use the increasing voltage program. This program allows the user to choose a constant pulse duration and apply that pulse with increasing amplitudes. However, the accuracy of the pulse parameters can vary. For instance, when using option (2), holding the duration constant, the amplitude increments can vary. For most of the experiments, the amplitude increase was set at 0.1 system volts, Vs, 0.25 magnetic volts Vm (as result of the magnification as discussed later). That is, as each pulse is sent the amplitude is magnified by 2.5, resulting in minimum increments of 0.25 V. It is possible to program smaller increments, however doing so causes increased inaccuracy in the pulse durations. Also while using option (3), holding the amplitude constant with increasing durations, the pulse durations can fluctuate significantly in a non-predictable pattern. A balance is needed between amplitude increments and timing increments that will produce accurate and repeatable results. It is not really understood why this happens. This is compensated for by repeating each run several times until 3 like results are achieved. This helps to ensure that there were no fluctuations that caused greater values in either time or amplitude to cause the particle to dislodge.
The second program used is a simple read in program. The voltage across the electromagnet is measured using the circuit described later and then reported back to the computer. This data is sampled using hardware timing (highly accurate as discussed earlier) at a rate of 2000 S/s. This data is graphed for visual comparison and also saved in a LabVIEW measurement file, a tab delimited text file. This file contains the relative time of the sample taken and the value of the voltage at that time. This allows a record of pulse durations accurate to the 0.0005 second. It is possible to read in data at faster rates, however, this affects the software timed program and reduces accuracy. After testing several different sampling rates, 2000 S/s was determined to be the fastest rate not causing loss of accuracy in the pulse generation program. As described previously, the NI-DAQ Pad 6015 has an accuracy of ±0.000305 V and each reading will give a value down to the microvolt.

Amplification Circuit

The most time consuming aspect of the preliminary work and experiment development was the design and fabrication of the amplification circuit that connects the data acquisition system and the electromagnet. The DAQ system is only capable of sending signals between ±10 V. At the beginning of the experiment design it was not known what range of voltages would be needed to dislodge the particle from its pocket at very short durations, but an assumption was made that it could be more than 10 V. A system was needed that would amplify the analog signal to an appropriate range to move the particle, measure the change in voltage across the electromagnet and then de-amplify the readings to an appropriate range that could be read by the DAQ system.
The first step in choosing amplifiers for the circuit was to determine some basic characteristics that would be ideal for the amplifiers. In electronics, an electromagnet is modeled as a resistor and inductor in series. A digital multimeter was used to determine both the resistance and inductance of the electromagnet, which were determined to be 41.5 Ohms and 0.054 Henrys respectively.
A second point was determining the maximum voltage rise time needed for the circuit. The voltage rise time is just as it sounds, the time needed for the voltage to rise to a certain amplitude. As this is just a rough value to be used in amplifier selection, exact values were not needed and maximum desired values were used. To simplify matters, the signal was also assumed to by sinusoidal. With this, the signal can be expressed as V(t) = A sin ωt (III.2)
where V(t) is voltage at time t, A is the amplitude of the signal in volts, ω is the frequency of the signal in rad/s and t is time in seconds. In order to minimize the voltage rise time, greater than maximum values were used. An assumption of 50 V as the amplitude and a signal frequency of 5000 /s were used. This results in V(t) = 50 sin (2π5000)t (III.3)
Voltage rise time can be determined by taking the derivative of this equation. The maximum voltage rise time would be where that derivative is at its maximum or when the second derivative is equal to zero.
dV/dt = (50)(2π5000) cos(2π5000t) (III.4)
where dV/dt is at its maximum when cos (2π5000t) = 1; when t = 0, therefore maximum rise time = (50) (2π5000) = 1.5 V/μs.
Up to this point in the design, the circuit was merely considered to be a black box type of connector between the DAQ system and the electromagnet; at this point it was necessary to decide exactly what the circuit needed to accomplish and how. Figure III.1 is a schematic of the finalized circuit which includes three amplifiers. The triangles symbolize the amplifiers. The first amplifier increases the voltage from the DAQ, the second amplifies the voltage differential across a small resistor which returns the current felt by the electromagnet, and the third follows a voltage divider which returns the an amplified voltage felt by the electromagnet. With this information, a line driver was chosen to run the circuit.
The line driver, chip, that was recommended for this circuit was the AD8392 from Analog Devices, Inc. This chip was chosen for its very high slew rate, also known as voltage rise time, and its ability to produce high currents while using low power levels. Another significant feature of this chip was its inclusion of 4 amplifiers; all of the amplification could be routed through one chip. The chip operated with either single or dual power supply and was capable of a peak linear output current of 400 mA.
The next step in the development process was the design and construction of the circuit board. The design was completed using an electronic circuit board layout design program, Eagle version 4.15. Eagle is a CadSoft USA product which allows the user to create a schematic of the circuit board as seen in Figure III.2 and then converts that into the necessary CAD files needed for construction. The program also checks for electronic errors and design rule errors. Figure III.3 shows the board layout design developed by Eagle. Once the final board CAD file is created the program then generates CAM files from the board design. These CAM files are standard files used in board construction that include information on design, layout, soldering, layers, copper, drill hole locations, etc. These files were then sent to Advanced Circuits, a company who constructs the actual circuit board. The files are then checked again by Advanced Circuits, once the files are approved, the board is constructed.
The last steps in production of the circuit board were done at the Unmanned Research Laboratory at Virginia Tech. All of the circuit’s pieces are surface mountable and must be soldered on. This allows for changes to be made to the circuit if certain parts of the design prove ineffective and require replacing. At this point, resistor values were chosen that would provide a 2.5 gain to the input voltage and then sufficient reductions to be sent back to the DAQ; meaning that a 1 V signal from the DAQ would produce 2.5 V signal to send to the electromagnet. Once all the resistors, the line driver, and connecting wires were soldered into place, the board was then tested with simulated signals and oscilloscopes to test for correct measurements.
One of the largest problems with these experiments was that without having any previous experiments for comparison, it was impossible to tell whether the circuit would be capable of producing the results needed; when testing using the electromagnet and sample balls began, it was decidedly incapable. Many problems arose with the first circuit design which evolved into many weeks of trial and error changing settings to achieve the desired results. The most frequent problem was overheating of the chip. As described earlier, the peak output current of the line driver was 400 mA. It was expected that the electromagnet would require approximately 350 mA, running the chip near its peak for long periods of time seemed to cause the chip to overheat frequently. The chip often burned out completely or shorted requiring a change in chip.
A second problem with the design resulted from the power supply. The circuit was being run with a single power supply, meaning it could provide only positive voltages. The chip, when run on a single power supply is able to produce voltages between 0 and 24 V with an actual max voltage swing of 23.0 V meaning the chip would never actually be able to reach its rails. During testing it was found that the lower rail of 0 V was much higher than anticipated, nearly 1 V, which when magnified was sometimes enough to remove the particle, thereby defeating the purpose of the experiments. It was necessary to have the resting voltage as close to 0 V as possible. The solution to this problem was adding a DC-DC converter to the circuit. This piece, the PT5062, a ±15 V DC-DC converter from Texas Instruments takes in the power from a single power supply and converts it to a dual power system. The dual power system now has rails of ±15 V (the chip actually has rails of ±12 V for dual power operation) and allows for absolute zero values, however it does reduce the upper rail from 24 V to 12 V which corresponds to a reduction in the amount of electromagnetic force able to be created.
The DC-DC converter circuit was then added to the original circuit, however many of the original problems with overheating and burning of the line driver still remained; the solution to this problem was more involved, requiring a completely new circuit with different line drivers. It was decided to use two separate line drivers to accomplish the amplification. The voltage amplification of the input signal required the most power and produced the most heat and so a second chip was added to handle this. The THS6182 from Texas Instruments is a low-power dissipation ADSL line driver. Not only significantly larger in size allowing for more heat dissipation, but the THS6182 also has a higher peak output current of 600 mA and a larger voltage output swing of 44 Vpp. The voltages from the voltage drop and voltage divider were then handled by a separate operation amplifier, the OPA2251 also from Texas Instruments. The OPA2251 is also larger in size than the original line driver and has a dual supply range of ±18 V. The switch to these two new op-amps required the design and construction of a new circuit board using Eagle; the DC-DC converter was also included on the new board. Figures III.4 and III.5 show the schematic and board layout for the final amplification circuit.
Once all the components of the final circuit board were soldered, tests were conducted at the Unmanned Research Laboratory with simulated signals. The new circuit was able to handle the heat and high power levels much better than the previous board. The limiting device was now the DC-DC converter with rails of ±15 V. During testing it was found that voltages in the 12.5-15 V range were often not resulting in the correct gains. Additionally applying power to the circuit without sending a signal causes high currents and high power levels that can damage the chip if run for significant portions of time. Also, the electromagnet should only be connected to the circuit after the power is turned on.
The second circuit that was designed was the final circuit used in these experiments. As noted earlier, conducting these experiments with no prior knowledge as to the desired outputs, much of the design was trial and error. The final circuit produces nearly the highest amount of power capable from a non-professionally design circuit. Voltage and current peaks higher than the ones available from this circuit will require a greater power supply and circuitry only available from a circuit board manufacturer. This circuit is suitable for these first experiments, however, if ever completed again; a professionally designed and constructed board would be a recommendation. Figure III.6 is a photograph of the entire experiment system setup.

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Circuit Parameters and Testing

The previous section described in detail the elements comprising the electronic circuit controlling the electromagnet. This section will give some detail as to the parameters set for these experiments and their bearings on the results.
A frequency response test was done to help determine the degree of accuracy that will be achieved for measuring the time durations of each pulse. The DAQ system has the capability of reading in voltages at a rate of 10 kS/s. Three sample tests were run at this rate, to show how voltage rise time varied with different amplitudes, this helps to determine the accuracy of the durations. Three different amplitudes were used 2.5 V, 6.25 V, and 12 V covering the range of amplitudes used during the experiments. Each pulse was sent for a duration of 6 ms. Figures III.7 – III.9 show the data taken for a single pulse. For both 2.5 V and 6.25 V the frequency response is approximately 0.2 ms, for the 12 V case, the response time increased to nearly 0.4 ms. Each of these however, is less than the error due to the chosen sampling rate of 2000 S/s.

Ball Placement

As electromagnetic fields cannot be seen, it was important that for each experiment, the location of the moveable particle be known and at the same location in repeated experiments. The moveable balls are each spherical with diameters of 4 mm, 6 mm, and 8 mm. The base balls are the same, only Teflon. In order to maintain consistency for the experiments, the location of the center of the moveable ball was kept track of and used for alignment.
Three separate bases were created to be used for these experiments. The bases consist of four equal diameter balls in a tetrahedral arrangement. These balls are then affixed to an aluminum plate. This plate is then affixed to the top most stage in the stabilization structure. From this point, the moveable particle is aligned to the center of the core of the electromagnet. An aluminum pin is affixed to the top of the electromagnet parallel to the center of the core. This pin is used to find the center of the pocket of the base balls through which the moveable ball will roll. The base is laterally adjustable for this alignment. Additionally, to align the center of the moveable ball to the center of the magnet core, the ball is placed in the pocket and vertical stage measurements are taken at the top and the bottom of the ball using the pin. The distance from the pin to the center of the core is known and a vertical alignment can be made. The third and final alignment is the distance from the face of the magnet. As mentioned earlier, the air gap between the attractable object and the electromagnet is very important. The greater the air gap, the less force produced. With this variation in force, it would be nearly impossible to compare the result of these experiments. Seven different sets of experiments were conducted; five of these sets were completed with the center of the moveable ball being at the same distance from the face of the electromagnet. The first basic experiments were done with the moveable ball and the base balls of equal diameter. The base balls were located such that the fronts of the base balls were touching the face of the electromagnet. Additionally, four more experiments were run with different combinations of ball and base diameters. Each of these experiments was run at an equal distance from the front of the electromagnet for better comparison.
Although great care was taken to insure the location of the center of the moveable ball was consistent for each experiment, a check was done to see what might occur if the moveable ball were off center. Measurements of a “steady state” condition were taken while the ball was at center and at varying distances off center until the ball was over half a ball diameter off center. The voltages required to move the ball remained the same. It was then determined that the location of the ball laterally was not as important as the distance of the ball from the face of the magnet.

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Table of Contents
ABSTRACT
Acknowledgements
Table of Contents
List of Figures
List of Tables
Nomenclature
Introduction and Literature Review
I.1 Sediment Transport in Nature
I.2 Traditional Sediment Transport
I.3 Turbulent Flow and its Effect on Sediment Transport
I.4 The Stochastic Method
I.5 Study Objectives
Experimental Facilities
II.1 Experiment Components and Setup
II.2 Electromagnet and Particles
II.3 Data Acquisition System and Pulse Generator
II.4 Amplification Circuit
II.5 Stabilization Structure
II.6 High Speed Camera
Preparatory Work
III.1 Electromagnet
III.2 Signal Programming
III.3 Amplification Circuit
III.4 Circuit Parameters and Testing
III.5 Ball Placement
Analysis and Results
IV.1 Introduction
IV.2 Particle Motion
IV.3 Electromagnetics
IV.4 Voltage and Force Correlation
IV.5 Incipient Motion Experiments
IV.6 Force-Time Relationship
Preliminary Camera Work
V.1: Introduction
V.2: Initial Digital Imagery
V.3: Methods and Procedures
V.4: Analysis and Results
Conclusions and Recommendations
VI.1: Electromagnetic Experiments
VI.2: Preliminary High Speed Camera Work
VI.3: Recommendations
References
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