Master’s Thesis in Engineering Physics, 30 ECTS Master of Science in Engineering Physics, 300 ECTS
Autumn term 2018
Development of a Mobile Reactor for Large
Scale Water Treatment
Development of a Mobile Reactor for Large Scale Water
Treatment
Alexander Berggren
c
⃝ Alexander Berggren, 2019.
Examiner: Krister Wiklund, Department of Physics. Supervisor: Mattias Ekström, SpinChem AB.
Internal supervisor: William Siljebo, Department of Chemistry.
Master’s Thesis in Engineering Physics, 30 ECTS. Department of Physics.
Umeå University.
SE-901 87 Umeå, Sweden. Phone: +46 90-786 50 00.
First of all would I like to thank my supervisor Mattias Ekström at SpinChem AB. He has supported and guided me through this whole project and answered all my questions whenever I needed help. I would also like to give a special thanks to Erik Löfgren for helping with ideas, Emil Byström for helping me with testing the mobile reactor, Christo-pher Öberg for helping me with the final pictures and Edith Björnberg Kalén for all the advice and good talks.
I would like to show my gratitude towards Peter Wikström at Umeå University who helped me with parts of the construction, William Siljebo who helped me with this report and my examiner Krister Wiklund who guided and advised me trough this project. Finally I want to thank my family and especially my girlfriend Karolina, for your un-conditional support during these years of studies and now my final master thesis work. I could not have done it without you.
Water pollution is one of many environmental problems that currently exists and inade-quate treatment of industrial wastewater is contributing to further pollution. SpinChem AB’s Rotating Bed Reactor (RBR) technology offers the possibility of water treatment by carrying out reactions between a solution and a solid phase. To move further in the field of large scale water treatment, SpinChem AB developed a prototype of a mobile reactor, i.e. a raft, carrying the RBR technology. The prototype proved that a mobile reactor can greatly reduce the process time for larger water volumes compared to a stationary RBR. The aim of this thesis is to develop the next version of the mobile reactor, with increased operational stability and autonomous driving (autopilot) as main goals. This work covers all parts in the development of the new mobile reactor which involves design, simulation, construction, electronics, software implementations and testing. The presented mobile reactor is a twin hull surface vehicle with the possibility of using two RBRs for water treatment. The steering is based on differential motor thrust and the autonomous driving was achieved using sensor data from a GPS, magnetometer and accelerometer, together with a proportional-integral-derivative (PID) type control system. The autopilot was put to the test on two different travel routes with a P and PI controller. The mobile reactor successfully followed the given routes, thus verifying that the developed mobile reactor can be used for future autonomous large scale water treatment.
Vattenförorening är en av många nuvarande existerande miljöproblem och en otillräcklig behandling av industriellt avloppsvatten är en bidragande faktor till fortsatta föroreningar. SpinChem ABs roterande bäddreaktor (RBR) erbjuder möjligheten till vattenrening genom att möjliggöra reaktioner mellan en lösning och en fast fas. För att ta nästa steg inom storskalig vattenbehandling har SpinChem AB utvecklat en mobil reaktor, en flotte, som använder sig av RBR-teknologin. Prototypen visade att behandlingstiden för större vat-tenvolymer kan minskas drastiskt genom att använda en mobil reaktor jämfört med en sta-tionär RBR. Syftet med detta examensarbete är att utveckla nästa version av den mobila reaktorn, med huvudmålen att den ska ha en ökad stabilitet vid drift och ha möjligheten till att vara självkörande (autopilot). Detta arbete involverar alla delar i utvecklingen, vilket handlar om design, simulering, konstruktion, elektronik, implementation av mjuk-vara och testning. Den färdiga mobila reaktorn består av ett tvådelat skrov med plats för att använda två RBR:er för vattenrening. Styrningen är baserad på att differentiera kraften till motorerna och autopiloten använder sig av tre sensorer, en GPS, magnetometer och accelerometer, tillsammans med en proportionell-integration-derivering (PID) regulator. Autopiloten blev testad med en P- och PI regulator på två olika färdvägar. I båda försöken lyckades mobila reaktorn följa den givna färdvägen, vilket verifierade att den utvecklade produkten kan användas till autonom storskalig vattenbehandling.
CFD Computational Fluid Dynamics ESC Electronic Speed Controller GPS Global Positioning System I2C Inter-Integrated Circuit Li-Po Lithium-ion Polymer NED North-East-Down
PID Proportional-Integral-Derivative PVC Polyvinyl Chloride
RBR Rotating Bed Reactor RPM Rotations Per Minute SST Shear-Stress-Transport TSP Traveling Salesman Problem
1 Introduction 1 1.1 Background . . . 1 1.2 Aim . . . 1 1.3 Goals . . . 1 1.4 Limitations . . . 2 2 Theory 3 2.1 Buoyancy . . . 3 2.2 Coordinate system . . . 3 2.3 Tilt-compensated magnetometer . . . 4
2.3.1 Hard- and soft iron distortions . . . 5
2.4 Accelerometer . . . 6
2.5 Autopilot . . . 7
2.6 Control system . . . 8
2.6.1 The controller . . . 9
2.7 Fluid dynamics . . . 9
2.7.1 Dimensionless distance from walls . . . 10
2.7.2 Drag coefficient . . . 11
2.8 Rotating Bed Reactor . . . 11
3 Method 13 3.1 Pontoon . . . 13
3.2 Numerical investigation of pontoon design . . . 16
3.2.1 Geometry . . . 16
3.2.2 Mesh . . . 17
3.2.3 Boundary conditions & fluid properties . . . 19
3.2.4 Steady state & transient solution . . . 19
3.2.5 Mesh convergence . . . 20 3.3 Deck . . . 20 3.4 Cover . . . 21 3.5 Electronic equipment . . . 22 3.5.1 Magnetometer calibration . . . 25 3.6 Autonomous driving . . . 26 3.7 Experimental testing . . . 28
3.8 Routine for choosing travel route . . . 28
4 Results 30 4.1 Mobile reactor . . . 30
4.2 Results from numerical test of pontoon design . . . 31
4.3 Calibration of magnetometer . . . 33
4.4 Current measurements . . . 34
4.5 Experimental test of autopilot . . . 34
4.6 MATLAB routine . . . 36
5 Discussion and conclusion 37 5.1 Mobile reactor . . . 37
5.1.3 Material and products . . . 38 5.1.4 Electronics . . . 39 5.2 Autopilot comparison . . . 39 5.3 Future implementations . . . 40 5.4 Assessment of goals . . . 40 5.5 Conclusion . . . 41 References 42 Appendix A Blueprints i
Appendix B Circuit diagrams iv
Appendix C List of inventory v
Appendix D Radio controller vi
1
Introduction
1.1
Background
There are many environmental problems that our earth currently faces, one of them is water pollution. Heavy metals in mining ponds and radioactive water are just two areas where polluted water exists. To reduce further pollution, it is critical that all industrial wastewater has adequate treatment before it is being released. According to [1], about 56% of the global freshwater withdrawals are returned as wastewater and at the same time there are estimates that over 80% of that wastewater is not adequate treated before it is released into the environment. Water purification is one of the areas where the Rotating Bed Reactor (RBR) technology, developed by SpinChem AB, is useful. The RBR consists of a rotating cylinder with a solid phase packed inside. The rotation of the RBR produces a fluid flow through the cylinder where reactions occurs between the solution and solid phase[2].
One great benefit of using an RBR compared to other techniques is that the solid phase is always contained inside the rotating cylinder, which makes replacement of the solid phase a relatively easy procedure. A different water cleaning technique, commonly known as a continuous stirred tank reactor, works similarly as for the RBR. The difference is that the solid phase is directly added into the solution and the whole mixture is stirred with an impeller. Such a method needs additional work for separating and continuously removing the solid phase from the solution[3]. For larger water volumes, such as a pond, it becomes a highly impractical method. Once the solid phase is placed into the pond, there is no easy way of removing it, thus making the RBR technology the preferable choice.
To move further in the field of water treatment, SpinChem AB has developed a prototype of a mobile reactor, i.e. a raft, carrying the RBR technology. The prototype showed that the process time for large water volumes could be greatly reduced by using a mobile reac-tor instead of a stationary RBR[4]. In addition to reduced process time, a mobile reacreac-tor is useful in situations and places which are dangerous to humans, such as radioactive wa-ters. It is now time to take the next step towards a final product, creating the next version of the mobile reactor with added functionality.
1.2
Aim
The aim of this master’s thesis is to further develop the mobile reactor to a viable product, including at least one mounted RBR for processing water bodies. It should be operable by both radio control and autonomous driving (autopilot) in water conditions resembling an indoor pool environment.
1.3
Goals
1. Construct a stable hull which allows for safe and stable operations in water condi-tions resembling an indoor pool environment.
2. Implement manual (radio-controlled) and autonomous (GPS-controlled) driving. 3. Implement a routine for choosing travel route given an area of operation.
4. State estimates for the time needed for the raft to process a given body of water.
1.4
Limitations
There are no requirements that the mobile reactor should be able to withstand heavy wind and waves, as the indented field of deployment is calm waters. There is also a budget limitation where the cost of additional parts for the new mobile reactor, should not exceed 10 000 SEK.
2
Theory
2.1
Buoyancy
The mobile reactor to be developed within present project is a surface vehicle and thus affected by fluid forces and motions. Any object placed in a liquid is subject to an upward force called buoyancy. This comes from Archimedes famous principle[5]: The buoyancy
is equal to the weight of the displaced liquid. This means that in order for an object to
stay afloat, the net force has to be zero, i.e.
Fnet= mg−ρfVdispg = 0 (1)
where m is the mass of the object,ρf the density of the fluid, Vdisp the displaced volume
of fluid and g is the gravitational acceleration. Rearranging Eq.(1) gives
m =ρfVdisp (2)
which can be used for determining the maximum load an object can hold while still staying afloat.
2.2
Coordinate system
One of the goals in this work is to make the mobile reactor autonomous, which means that its position and orientation needs to be known at all times. A common coordinate system used in aerospace and for surface vehicles is the north-east-down (NED) convention. The NED coordinate system can be seen in Fig.1 where x is the travel direction for the body and z is down towards earth. The rotations of pitch, roll and yaw can also be seen in the figure. Yaw is also known as, and will be referred to as, heading. Pitch, roll and heading are denoted asθ,ϕ andψ, respectively.
x
z
y
yawroll
pitch
Figure 1– Illustration of the NED coordinate system where x is the direction of travel and
z is the direction down towards earth. The image also shows the definition of pitch, roll
All coordinate systems will hereon follow the NED convention if nothing else is stated.
2.3
Tilt-compensated magnetometer
A magnetometer is a simple instrument that measures the surrounding magnetic field and can thus be used to find the mobile reactor’s steering direction, or heading. To calcu-late the heading of a body, one must measure the component of Earth’s magnetic field which is parallel to the ground, Bxy. If we assume that the magnetometer body is not
tilted relative to the ground, i.e. pitch and roll is zero, then the heading is defined as the angle shown in Fig.2. Mxand Myare the magnetometer readings in the x and y direction,
respectively, which are values proportional to the magnetic field strength. A magnetome-ter generally outputs a voltage proportional to the magnetic field strength, which has to be converted for the reading to have any meaningful unit. Since the conversion is not made in this work and the unit does not matter for the application of the magnetome-ter, the magnetometer readings will hereon be considered as a unitless quantity that is proportional to the magnetic field strength.
x
y
B
z
ψ
xy Mx MyFigure 2– A non-tilted magnetometer with the corresponding coordinate system and
head-ing.
The heading can simply be calculated as
ψparallel= atan2(−My, Mx), (3)
where atan2(−My, Mx) computes the polar angle arctan(−My, Mx)[6]. The advantage of
using this function is that it keeps track of the signs of each term and can thus determine which quadrant the result is located in. Note that the heading should be a value between 0-359◦ with clockwise rotation increasing the heading, thus the minus sign for My. To
achieve values between [0◦,360◦), one has to add 360◦ifψparallel< 0.
readings of Mxand Myare not in the same plane as Bxy. Fig.3 shows a tilted magnetometer
where the readings are along x, y and z. In order to use the same formula for this case as in Eq.(3), the magnetometer readings needs to be compensated for the pitch and roll.
y
y
′z
′z
x
x
′ϕ
θ
MagnetometerFigure 3– A tilted magnetometer with non-zero pitch and roll.
The compensated readings are obtained as
Mx′= Mxcosθ+ Mzsinθ
My′= Mxsinθsinϕ+ Mycosϕ+ Mzcosθsinϕ
(4)
and thus a tilt-compensated heading is expressed as
ψ = atan2(−My′, Mx′). (5)
2.3.1 Hard- and soft iron distortions
Since the magnetometer measures the surrounding magnetic field, it will not only mea-sure Earth’s magnetic field, but it will also suffer nearby distortions. These distortions are generally classified as either hard- or soft iron distortion[7]. Hard iron distortions arises from materials that themselves generate a magnetic field, such as a permanent magnet or other ferrous materials, that adds to Earth’s magnetic field. Soft iron distortions instead alters the existing magnetic field in some way and comes from surrounding metals such as iron.
Fig.4 shows the effect on the magnetometer readings in case of distortions when a mag-netometer is rotated in the horizontal x-y plane and the z-component has been neglected. Soft iron distortions gives the elliptical shape while hard iron produces the offset[7]. The ideal readings in 3D-space is a sphere centered at origin.
-50 0 50 100 -40 -20 0 20 40 60
Figure 4– Magnetometer readings for rotation in the x-y plane showing both ideal
mag-netometer readings when there is no distortions (stars) and also readings with hard- and soft iron distortions (rings). Note that the values are arbitrary chosen.
It is possible to remove the distortions by calibrating the magnetometer. By finding the offset and scale factors for re-scaling the ellipse to a circle, calibrated readings can be determined as follows
Mx∗= cx(Mx− kx) My∗= cy(My− ky) Mz∗= cz(Mz− kz)
(6)
where cx, cy, cz are the scaling factors in each direction and kx, ky, kz are the offset
constants.
2.4
Accelerometer
A tilt compensated heading is only obtainable if pitch and roll can be determined. One way of calculating them is to use an accelerometer which measures acceleration, such as the gravity of Earth. A three axis accelerometer will measure three values, Ax, Ay
and Az in the x, y and z direction, respectively. The values will depend on how much
the accelerometer is tilted relative to earth. If the z-component is pointing down toward earth, the Azcomponent will measure the gravity of Earth while the two other components
measure zero.
Aligning the accelerometer coordinate system with the magnetometer shown in Fig.3, one can directly obtain the pitch and roll as
θ = atan2(Ax,−Az) ϕ =−atan2(Ay, √ A2 x+ A2z)) (7)
2.5
Autopilot
An essential part of an autopilot is to make the mobile reactor autonomously follow a designated path. The parameters that the autopilot has to know is the current location and heading as well as the target location and desired heading. A common situation for an autopilot system is shown in Fig.5. A device, such as a mobile reactor, is currently located at longitude and latitude (φ1,λ1) with a current heading ofψc. The target location
is situated at (φ2,λ2) and the desired heading of the system is ψd. The heading error is
then simply given by
e =ψd−ψc. (8) ( , )φ2 λ2 N Current heading Desire d head ing ψc ψd e
( , )
φ
1λ
1Figure 5– Illustration of a common situation for an autopilot system where the heading
of the device is not aligned with the desired heading.
The current heading have to be measured by the device itself, using for instance a mag-netometer. The desired heading can however be obtained by using the current position and the target position, as follows
where∆λ =λ2−λ1[8].
In addition to knowing the heading error towards the desired location, the distance is also of importance. Knowing when the device has reached its target location is for obvious reasons, a necessity. The distance between two coordinates on earth can simply be de-rived from basic trigonometry with good precision, if the two points are fairly close to each other. An even better formula is the haversine distance formula which takes into that the distance between two coordinates on earth is actually an arc. The haversine distance formula can be written as
d = 2R sin−1 (√ sin2 ( ∆φ 2 )
+ cosφ1cosφ2sin2
( ∆λ
2 ))
(10)
where R is the radius of Earth and∆φ=φ2−φ1[11].
2.6
Control system
A control system is used to change the behavior of the mobile reactor such that it can reach its target coordinates. A feedback control loop, shown in Fig.6, can be used to autonomously control a system while also reducing the impact of any disturbances that enters the system[9].
Controller Actuator System
Disturbances u(t) Measurements r(t) e(t) y(t) − ym(t)
Figure 6– A feedback control system
The desired system output y(t) is represented by the reference signal r(t), also known as the setpoint. The error of the system is given by
e(t) = r(t)− ym(t) (11)
where ym(t) is the measured value of the system output together with any measurement
passed to an actuator which physically affect the system state. For a mobile reactor the actuator can for instance be the rudder or the rotations per minute (RPM) of the motors. 2.6.1 The controller
There are numerous different controller types and a common one is the proportional
-integral - derivative (PID) controller. The control signal is based on the error signal and
can be written as u(t) = kpe(t) + ki ∫ t 0 e(τ)dτ+ kd de(t) dt (12)
where kp, kiand kd are constants[10]. Depending on the chosen values of kp, ki and kd,
one will get a different type of controller, for instance using kd = 0, kp̸= 0 and ki̸= 0
gives a PI controller.
One well known phenomena that one has to consider when dealing with the integral term is windup. It can happen that the control signal reaches the actuator limits and if the controller uses the integral part, this will continue to integrate and thus wind up and the control signal becomes very large. Since the actuator limit has been reached, a larger control signal will have no additional effect on the system. If no precautions are made, the error has to have the opposite sign for the same amount of time for the integral term to return to its normal state[9]. To deal with this issue one has to apply some kind of anti-windup procedure to limit the integral part. One way of doing it is to set bounds for the control signal and if the signal becomes larger than the bound limit, the integral term is reduced.
2.7
Fluid dynamics
To find an efficient shape of a surface vehicle like the mobile reactor, one needs to in-vestigate the fluid forces affecting the vehicle. Many fluid flows can be described by Navier-Stokes equations. The equations describes the motion of a viscous fluid and can be derived by looking at the balance of momentum of a fluid element, i.e. a small volume of fluid containing millions of molecules. The Navier-Stokes equations for an incom-pressible fluid can be described as
ρ ( ∂ui ∂t + uj ∂ui ∂xj ) =−∂p ∂xi + ∂ ∂xj ( µ∂ui ∂xj ) ∂ui ∂xi = 0 (13)
where u is the flow velocity, p is the pressure, ρ is the fluid density, µ is the dynamic viscosity and i, j are indices following Einstein summation convention[12].
Computational fluid dynamics (CFD) is a tool to simulate flows described by Eq.(13). Simulating turbulent flows directly from Navier Stokes equations is usually too computer expensive for any practical use. Therefore, different turbulent models have been de-veloped by time-averaging, ensemble-averaging, or otherwise manipulating the Navier-Stokes equations[13].
All turbulent models have its strength and weaknesses and many of them are often char-acterized as either a near-wall turbulence model or a free-stream model where the latter is intended for flows in the far field, i.e. far from any boundary. The model considered in this work is the Shear-Stress-Transport (SST) k-ω model which is a model where you get the best of both worlds. In the near-wall region, it uses k-ω model designed for this region and far from any boundary it uses the free-stream k-ε model. The model uses a special blending function which activates the k-ω in the near-wall parts of the flow and
k-ε in the far field[14].
In this work the SST k- ω model is used the get an estimate of the drag coefficient for different shapes of a pontoon. The exact equations behind the SST k-ω model is beyond the scope of this report, further information can be found in[14].
2.7.1 Dimensionless distance from walls
In turbulent flows there exist so called boundary layers in the region close to a wall. The flow have different characteristics in this region and when simulating a turbulent flow, one must consider how to deal with this part. The viscous sublayer is the layer closest to the wall. The width of this sublayer is defined using a dimensionless distance from the wall defined as
y+= ρ u∗y
µ (14)
where u∗is the friction velocity at the nearest wall and y in this case represent the perpen-dicular distance from the wall[15]. The viscous sublayer is in the region where y+< 5.
When a near-wall model is used, as for the SST k- ω model, one must use a mesh fine enough to resolve the viscous sublayer and a recommendation is that the first mesh element should be on the order y+ = 1[16]. It is possible to estimate what size the first
mesh should be in order to resolve y+= 1. Let y1be the height of the first mesh element,
then Eq.(14) can be rearranged as
y1= y+µ
ρu∗. (15)
u∗= √
τω
ρ (16)
whereτω is the wall shear stress and can be computed from the skin friction skin friction coefficient Cf as
τω =1 2CfρU
2
∞ (17)
where U∞is the free-stream velocity[17, 18, 19]. Finding en estimate for y1comes down
to estimating Cf. There are many different estimates for Cf based on empirical results
and one of them is
Cf = 0.0576Re−0.2 (18)
where Re is the Reynolds number defined as
Re =ρU∞L
µ (19)
and L is the characteristic length [19, 20]. 2.7.2 Drag coefficient
Drag coefficient is a dimensionless quantity that can be used to determine the resistance of an object submerged in a fluid. It can be expressed as
Cd=
2Fd
ρu2A (20)
where Fd is the drag force and A the reference area[21]. The drag coefficient is used in
this work to evaluate different designs of a pontoon. A smaller drag coefficient value implies a better streamlined body since it experiences a smaller resistance in the fluid.
2.8
Rotating Bed Reactor
The mobile reactor should be able to clean the water it travels through and this is achieved by using a Rotating Bed Reactor. The RBR, shown in Fig.7, is a product developed and produced by SpinChem AB. The RBR can be used for heterogeneous reactions and it typically enhances the mass transfer between a solution and solid phase[2]. The inside of the RBR consists of four compartments where the solid phase is placed. An inner
and outer filter is also used around the inside cylinder walls to keep the solid phase in place. Rotating the RBR creates a circulating flow through the RBR, by centrifugal forces, which allows reactions to take place between the reactants in the solution and the solid phase. Depending on the choice of solid phase, the RBR can be used for various applications, e.g using activated carbon for decolorizing liquids.
3
Method
The complete construction of the mobile reactor can be categorized into four parts: pon-toons, deck, cover and electronics. The next sections will cover each category followed by descriptions of the implemented software and of the experimental testing.
3.1
Pontoon
The floating capacity of the mobile reactor comes from its two pontoons made primarily out of polyvinyl chloride (PVC) pipes with a diameter of∅ = 160 mm and wall thickness of 5.9 mm. Each pontoon consists of two separate parts, a longer part with a length of 780 mm and a shorter part with a length of 180 mm. The shorter part holds the motors that drives the mobile reactor forward. A schematic of the two parts can be seen in Fig.8. As the figure also shows, there are three holes on top of the longer pontoon part where stainless steel bolts were placed to fasten three aluminum bars (further description in section 3.3). One end of each pontoon part was cut twice at 35◦angles relative the outer wall, creating a tip at both the front and back of the assembled pontoon. The 35◦angle cut was not chosen arbitrarily but rather based on simulation results, which are explained in section 3.2 below. The other end of each pontoon part was cut with a standard 90◦ angle. See Appendix A for more detailed blueprints.
Figure 8– Schematic of the two cut pontoon parts.
A brushless motor was placed on a 3D-printed motor holder, see Fig.9 for a schematic and Appendix A for blueprints, and then bolted tight at the bottom hole of the shorter pontoon part.
Figure 9– Schematic of the motor holder for the brushless motor.
The large hole on top of the smaller pontoon part was used to carry out cables connected to the brushless motor, while the smaller hole carries out two small cables used as a water sensor. The water sensor has a very simple design where two cables were placed close to each other, but not touching, at the bottom of the pontoon. The idea was to detect potential water leaks inside the smaller pontoon part. By setting a voltage of 3.3 V relative ground on one of the wires and measure the voltage on the other, one would measure zero voltage if there is no leak and 3.3 V if there is a leak. The water gives a connection between the two wires, thus measuring 3.3 V.
To hold the smaller and larger pontoon parts together, two sets of angle brackets were placed on each part with bolts holding the pieces together. The inside of the smaller pontoon part can be seen in Fig.10 where the water sensor, motor holder with brushless motor and also the angle brackets are shown. In order for the pontoon to float, the open ends had to be sealed. This was done using a 10 mm thick PVC-plate where matching pieces to each opening was cut out and then glued on and sealed with sealant. Given the dimensions of the pontoons, using Eq.(2) with standard water density, gives the mobile reactor a maximum mass of approximately 36 kg. This mass would however mean that the pontoons are completely below the surface, which is not ideal. A more suitable mass would be around 20 kg where the height of the pontoons are about 55% below the surface.
Angle bracket
Motor holder and brushless motor
Water sensor
Figure 10– Inside of the smaller pontoon part where the water sensor, motor holder with
brushless motor and the angle bracket is marked.
The final step of building the pontoons was to attach the propellers. To do this, a flexible shaft coupler was attached on the 8 mm shaft of the brushless motor. In the other end of the coupler, a stainless steel propeller shaft was placed which had an inner rotatable shaft of 4 mm and an outer fixed shaft of 8 mm. An 8 mm hole was drilled on the tip of the pontoon part, 40 mm up from the bottom, where the propeller shaft was pointing out, see Fig.11. Propeller grease was used around the inner rotating shaft and at the ends of the propeller shaft to prevent water leakage. A nylon propeller with a diameter of 55 mm was placed on the end of the propeller shaft. The propeller on each pontoon are opposite to each other since one is for clockwise rotation and the other for counter-clockwise. As you may have noticed, there was no rudder attached to control the steering of the mobile reactor. Instead, differential motor thrust has been used, which means that the steering is achieved by setting different RPM of each brushless motor.
Propeller
Propeller shaft
40
mm
Figure 11– Side view of the smaller pontoon part where the propeller shaft and propeller
is shown.
3.2
Numerical investigation of pontoon design
The goal of the simulations was to see how much Cddecreased for different cut angles at
the front and back of the pontoon. In total, five different cut angles were simulated in a 3D channel flow, namely 90◦, 70◦, 45◦, 35◦and 25◦. All simulations were performed in Ansys Fluent 19.0 using the default settings of the SST k-ω model.
3.2.1 Geometry
The simulated pontoons were somewhat simplified compared to the final build pontoon described in section 3.1, by disregarding all holes, angle brackets and propeller. All simulated pontoons were in a single piece with a total length of 900 mm and∅ = 160 mm, Fig.12 shows the shape of the simulated pontoon with a 35◦cut.
Figure 12– A schematic of the shape for the simulated pontoon. Here the cut is 35◦and a total length of 900 mm.
The simulation domain can be seen in Fig.13 where the radius of the channel is 3.2 m and length of 13 m. The front tip of the pontoon was placed 3.55 m into the channel. The domain is only for a half-channel, separated at the center axial plane, since the symmetry plane allows for the use of a symmetry constraint to reduce the computational load.
Figure 13– Simulated 3D channel domain.
3.2.2 Mesh
The domain was split into 12 sections, some of which are visible in Fig.13. The main objective of the split was to take advantage of the symmetry of the channel leading to faster meshing by using Ansys match control setting on the cone shaped domain pieces, but it also made it possible to refine the mesh surrounding the pontoon. For the general
mesh setting, a mesh with a maximum face size of 0.1 m and maximum tetrahedral size of 0.56 m was used, where a side view for the mesh can be seen in Fig.14.
Figure 14– Mesh for the side view of the domain symmetry plane.
The part surrounding the pontoon has a width and height of 1 m and length 2.7 m. The pontoon was placed in the center of the cuboid. First of all, the face sizing of the pontoon was refined to 3· 10−3 m. Further, the inflation option was used to define 10 boundary layers from the pontoon surface. To resolve the viscous sublayer, the intent was to have
y+= 1 around half way in the first mesh element, thus an estimate for first layer thickness
was calculated using Eq.(15)-Eq.(19). Using a free-stream velocity of U∞ = 0.3 m/s, characteristic length of L = 0.9 m, water densityρ = 998.2 kg/m3, viscosity µ = 1.003· 10−3 kg/(ms) and y+ = 2, gave a first layer thickness of y1≈ 1.38 · 10−4 m. However,
to be on the safe side, the first layer thickness was set to 1· 10−4 m. As it was checked during the simulations, the maximum y+value in the first cell was well below 2, therefore
no further refinement for the boundary layer was needed. A close-up on the mesh at the front of the pontoon can be seen in Fig.15.
Figure 15– Close-up on the mesh for the front tip of the pontoon.
3.2.3 Boundary conditions & fluid properties
A velocity inlet boundary condition was set on the channel edge closest to the pontoon in Fig.13, where the velocity magnitude was set to 0.3 m/s. The other edge of the domain has a pressure outlet boundary condition of 0 bar. Both the pontoon walls and domain wall parallel to the pontoon, have a non-slip boundary condition.
All simulations used Ansys Fluent 19.0 liquid water property which had the same values for density and viscosity as used in the first layer thickness calculation above.
3.2.4 Steady state & transient solution
Even though a turbulent flow has time dependent properties, it was expected that the drag coefficient would reach a steady state. This was expected since the largest difference between a steady state and transient solution, was likely the flow behind the pontoon which would likely have a negligible effect on the drag coefficient. If that was the case, a steady state solver can be used which drastically reduce the computational time. All five angles were computed with the same settings described above and using the steady state solver. The solution was iterated until the drag coefficient reached a stable value, which was obtained in between 1000-1500 iterations. The drag coefficient was calculated for the pontoon body in each iteration using an Ansys Fluent 19.0 built in function.
In order to confirm that the steady state approach was valid, a transient solution for the 70◦cut pontoon was also simulated. A time step size dt = 0.01 s was used with 20000 time steps in total, giving a flow time of 200 s. For the transient solution, the drag coefficient was calculated at each time step.
3.2.5 Mesh convergence
A mesh convergence study was also made on the pontoon with a 70◦cut angle. The face mesh of the pontoon was varied from 3· 10−3 m to 7· 10−3 m with steps of 10−3m. The point of this study was to see if the choice of mesh had any major effect on the end result.
3.3
Deck
To fixate the two pontoons relative each other, three aluminum bars with T-slotted ex-trusion was used and placed on the three bolts on top of each pontoon. The T-slotted extrusion made the bars slidable on the bolts which means that the width of the mobile reactor was adjustable. The middle bar has dimensions 40x40x56 mm and two other 40x40x60 mm. The front and back bar served another purpose as well. In the middle of the bars, a∅ = 26 mm hole was drilled 12 mm into the bar, where one bearing in each bar was placed, see Fig.16. The bearings were capable of rotating∅ = 10 mm shafts and were used as shaft guides for the RBR shafts.
T- slotted aluminum bars Bearings
Figure 16– Three T-slotted aluminum bars fastened on the two pontoons. A bearing is
shown in the middle of the front and back bar.
To rotate the RBRs, two DC motors with chucks have been reused from the first prototype and they are essentially two modified screwdrivers[4]. Each DC motor was mounted on two M10 stainless steel shafts with a 3D printed fixture holding the DC motor in place, see Fig.17. The fixture was placed such that the chuck of the DC motor was centered in the bearing opening, see Appendix A for more detailed hole placement. A 750x600x10 mm PVC plate was bolted together with the aluminum bars and used as a platform for electronic equipment. Openings were cut out around the attached DC motor which can be seen in Fig.17.
Attached DC motors
Figure 17– Two attached DC motors, centered at the bearings opening. Platform for
electronic equipment is also visible.
3.4
Cover
A protection cover made from 2 mm thick transparent polycarbonate plastic was placed on top of the deck. The cover was made out of three pieces, two of which were used as walls and the last piece worked as the ceiling, see Fig.18 for a schematic of the three pieces. The left wall had two holes where two power switches were placed. The complete cover was assembled using silicon at all contacting edges. Blueprints can be found in Appendix A. The tilted front of the cover was aligned at the front of the deck platform. The back of the cover was attached to the deck platform with two hinges, such that the cover could be opened in an easy fashion. At the cover front, an eccentric lock was used to keep the whole cover in place.
Figure 18– Schematic of the three pieces that formed the protection cover.
3.5
Electronic equipment
There are two separate power supplies that powers all electronic equipment on the mo-bile reactor. One of them, which will hereon be referred as the 11.1 V power supply, consisting of two parallel connected 3 cell lithium-ion polymer (Li-Po) batteries with a nominal voltage of 11.1 V and capacity of 6 Ah each. The second supply is a also a 3 cell Li-Po battery with 11.1 V nominal voltage but with a smaller capacity of 2.6 Ah. The second supply is connected to a voltage converter which outputs 5 V, thus this power supply will hereon be referred as the 5 V power supply. From the 5 V output, a LED light is connected with a 220Ω resistor in series. Both power supplies are connected to a power switch. Circuit diagrams can be found in Appendix B for both power supplies and a full list of all the electronic equipment is located in Appendix C.
The brain of the system is a Raspberry Pi 3 Model B which has control over all motors and sensors. To explain the complete circuit, it is easiest to first take a look at the circuit diagram in Fig.19. Notice that the 11.1 V supply was used for all motors which includes the electronic speed controllers (ESC) that controls the brushless motors. The 5 V supply was used to power the Raspberry Pi and also power the internal logic for all other chips and sensors.
Figure 19– Circuit diagram for the complete electronic system. The left and right paren-thesis refers the either the left or right pontoon, respectively, when viewed from behind.
Since the brushless motors are three phase motors, electronic speed controllers are used for controlling the speed. The speed is controlled by sending pulse-width modulation signals from the Raspberry Pi to the input of the ESC. The pulse-width is ranging between 1000-2000 ms where 1000 ms gives zero speed and 2000 ms maximum speed. Each time the ESC’s are powered up, a calibration procedure has to be made before being able to control the speed of the motors. The calibration is completed by sending the maximum pulse-width, 2000 ms, for two seconds, followed by the minimum pulse-width, 1000 ms, for additionally two seconds. A 10 A fuse was also placed between the 11.1 V supply and each ESC, in case the propeller gets entangled and a massive current spike occurs. The RBR motors are regular DC motors and can therefore be connected directly to a battery. However, to achieve some level of controllability, relays have been used for switching the power on and off. The normal mode of the relay is giving no power to the DC motors, but by applying 3.3 V from the Raspberry Pi to the input pin on the relay, power is provided to the motors. The DC motors are rated between 0-550 RPM, so giving full power will give maximum RPM.
Driving the mobile reactor remotely was achieved using a radio transmitter (radio control) and radio receiver. Since the Raspberry Pi control everything, the radio control has no direct control over the motors. Instead the receiver was connected to the Raspberry Pi which read the incoming signals and performed the appropriate action. See Appendix D
for radio control settings and available controls.
As mentioned in section 3.1, the water sensor consisted of two wires in proximity of each other and in total two water sensor was used, one for each pontoon. To limit the current output, a 68Ω resistor was connected in series with the wire having 3.3 V applied to it. The voltage level was measured relative ground on the other wire for each sensor. A 10 kΩ pull-down resistor was used on the measuring wire, but instead of using additional hardware, the internal pull-down resistor of the Raspberry Pi was used and accessed via software. A complete circuit diagram of the water sensor with the pull-down resistor can be found in Appendix B.
The autopilot is based on data from three different sensors, a magnetometer, accelerom-eter and GPS. A LSM303 chip has been used which is triple-axis magnetomaccelerom-eter and accelerometer. The LSM303 uses inter-integrated circuit (I2C) protocol for communica-tion, therefore this chip is connected to the pins on the Raspberry Pi that allows for this communication. The GPS is a version 3 of the Adafruit Ultimate GPS Breakout. The GPS uses universal asynchronous receiver/transmitter (UART) communication and thus, as for the LSM303, it is connected to the Raspberry Pi pins that handles this type of com-munication. An external antenna is also connected to the GPS for better sensitivity but also for easier placement on the mobile reactor.
All electronics were placed in a 340x230x130 mm protection plastic box. The pins of the Raspberry Pi were attached to a circuit board using a 40-pin breakout kit and every connection to the Raspberry Pi shown in Fig.19 was soldered on the circuit board. The final assembly in the protection box can be seen in Fig.20. Note that not all electronic equipment is visible since parts are stacked on each other.
Relays 2.6 Ah Li-Po Battery 6 Ah Li-Po Batteries LSM303 GPS
Figure 20– Final electronic equipment placed inside the protection box. Batteries, Relays,
LSM303 and GPS is marked in the image. The remaining equipment is not marked since they are poorly visible due to stacking.
3.5.1 Magnetometer calibration
Removing hard- and soft iron distortions comes down to finding the scaling and offset constants in Eq.(6). One way of obtaining them is to use the maximum and minimum values that the magnetometer can read for each axis. First, raw magnetometer data was sampled during 90 s while rotating the completed mobile reactor around all three axis. Let Mx,i, My,i and Mz,i be the set of sampled data. Each pair of sampled data forms an
kx=
max(Mx,i) + min(Mx,i)
2
ky=
max(My,i) + min(My,i)
2
kz=
max(Mz,i) + min(Mz,i)
2 ,
(21)
whereas the scaling factors was obtained as
cx= Mxyz ∆Mx cy= Mxyz ∆My cz= Mxyz ∆Mz (22) where ∆Mx=
max(Mx,i)− min(Mx,i)
2 ∆My=
max(My,i)− min(My,i)
2 ∆Mz=
max(Mz,i)− min(Mz,i)
2
Mxyz= ∆M
x+∆My+∆Mz
3 .
(23)
The scaling factors reduces the magnetic field reading for the axis that has a large differ-ence between the max and min value and similarly, increase the reading for an axis that has a small difference. This scales the ellipse to a circle with radius Mxyz.
3.6
Autonomous driving
The autopilot was based on data from three sensors, GPS, magnetometer and accelerom-eter. All code was developed using the programming language Python. The autopilot is given a list of waypoints, i.e. latitude and longitude coordinates, that the mobile reactor should follow. Every two seconds the autopilot will update the speed of each brushless motor, i.e. a sample time of two seconds, with the goal of minimizing the heading error to the waypoint. Once the mobile reactor is within 5 m of the waypoint, it will continue to the next waypoint. When the last waypoint has been reached, the mobile reactor starts over from the beginning. The DC motors are turned on once the first waypoint has been reached. The speed of the brushless motor are controlled using a PID controller. The
control signal in Eq.(12) has to be discretized for it to be possible to implement it in a computer. At time tn> 0, the discretized control signal is given by
ud(tn) = kpen+ ki n
∑
j=1 e(tj)(tj−tj−1) + kd∆e ∆t (24)where en is the current error given by Eq.(8), ∆t = tn− tn−1 and ∆e = en− en−1.
Dur-ing each update, a number of consecutive calculations are made, easiest explained in Algorithm 1 below.
Algorithm 1Calculations for updating the speed of each brushless motor.
1: Collect sensor data from the magnetometer and accelerometer.
2: Adjust for distortions using Eq.(6) and use θ and ϕ with Eq.(7).
3: Compensate for tilt using Eq.(4).
3.1: Calculate the current heading ψc for the mobile reactor with
Eq.(5).
4: Collect GPS data for the current location of the mobile reactor.
4.1: Calculate the distance, Eq.(10), to the waypoint. If the
distance is less than 5 m, continue with next waypoint.
5: Calculate the desired heading ψd to the waypoint with Eq.(9).
6: Calculate the error, Eq.(8), and feed it to the PID controller and calculate the control signal with Eq.(24).
7: Update the speed to the brushless motors with the control signal.
What should be noted is that the PID controller and control signal, change the speed relative to a base speed given to both brushless motor. The base speed was set with a pulse width of 1150 ms and is what keeps the mobile reactor moving forward. The control signal was added to the base speed for one motor and subtracted to the other, thus the PID controller only controls the steering of the mobile reactor. The heading error was adjusted such that it only gives values between (-180◦,180◦]. The sign of the heading error ultimately decides the sign of the control signal. Due to the adjusted heading error, the mobile reactor always turn either clockwise or counter clockwise, depending on the more favorable choice. Additionally, it has been added for turning purposes that if the heading error|e| > 40◦, the motor not needed for turning will be turned off. To handle the windup issue with the integrating term of the PID controller, a form of back-calculation have been used. A first calculation of the signal is made and if the signal is saturated, the integrating term will be reduced enough to make a second calculation of the control signal fall just below the saturation limit.
Since the autopilot is heavily relied on a good GPS signal and access to sensor data, a number of precautions have been implemented to force the mobile reactor back to radio
control mode if unexpected problems arise.
3.7
Experimental testing
Three different current measurements were performed using a digital multimeter. First, the current provided from the 5 V supply was measured when the program was running in radio control mode and all motors were on, meaning that all the electronic equipment being powered from the 5 V was consuming power. Secondly, the current for the pair of brushless motors was measured at different speeds. The test was performed when the mobile reactor was placed in a water container and the current was measured at 10, 20, 30 and 40 % of maximum power to the brushless motors. Lastly, the current for a DC motor was measured when rotating an RBR. The model used was the SpinChem⃝R
RBR S3 which has a diameter of 70 mm[22]. The RBR was filled with active carbon and rotated submerged in water during the measurement.
The autopilot maneuverability is dependent on the choices of the PID parameters kp, ki
and kd. To verify that autopilot worked as intended, a couple of test runs were made.
Two sets of PID parameters were tested where the first one was a P controller with kp
= 0.9 and the second test used a PI controller with kp = 0.9 and ki = 0.01. In each test,
the autopilot was given a route, i.e. a set of waypoints to follow, but since the tests were made at different occasions and locations, the courses were not the same. During the autopilot testing, there were no RBRs attached to the DC motors.
3.8
Routine for choosing travel route
Since the autopilot is in need of coordinates for knowing the path it should follow, a MAT-LAB script was developed for this purpose. The script needs some user input, namely a list of coordinates that defines the area of operation, i.e. the boundary which the mobile reactor can operate within. The user also have to input the minimum distance between waypoints and the maximum distance allowed between a waypoint and the boundary. The routine starts by creating a uniform grid of waypoints with a horizontal and verti-cal distance between waypoints equal to the minimum distance that the user has entered. Each waypoint that is outside or too close to the boundary is then removed. There are several different ways of obtaining a travel route with the remaining waypoints, but three methods are implemented in this work.
The first one is simply letting the user draw their own travel route, not restricted to the remaining waypoints. The remaining waypoints is only used to guide the user for suitable distance between waypoints. The second method is based on obtaining a travel route with the shortest distance, where each waypoint should be visited once and the route should return to the starting point. This problem might seem familiar to some of you, as it is the well known Traveling Salesman Problem (TSP). The problem is solved using Joseph Kirk’s TSP solver which uses a Genetic Algorithm and finds a near optimal shortest route[23]. The third method is a brute-force method that goes either row by row or column by column in a zigzag fashion. The decision between row by row or column by column is dependent on the shape of the boundary, if the boundary is longer horizontally,
the route will go row by row and vice versa. Once the route has visited all waypoint once, it will change direction, i.e. from horizontally to vertically or vice versa, and zigzag back to the starting point.
4
Results
4.1
Mobile reactor
As the construction of the mobile reactor was a large part of this work, most development regarding the mobile reactor have already been presented in the previous sections. How-ever the completed and final assembly of the mobile reactor can be seen in Fig.21. The final width of the mobile reactor was set to 720 mm.
Figure 21– Completed mobile reactor with a mounted SpinChem⃝R RBR S3.
A close up on the deck and cover, is shown in Fig.22, where the final placement of the two power switches, LED, electronic box and GPS antenna is more clearly shown.
Power switches LED
GPS antenna Electronic box
Figure 22– Close up on the final deck assembly where the power switches, LED,
elec-tronic box and GPS antenna is marked.
4.2
Results from numerical test of pontoon design
The simulation results for the drag coefficient against the different cut angles can be seen in Fig.23. The y-axis has been scaled with Cd90, i.e. the drag coefficient for the 90◦cut angle. The result from the transient solution is also shown and the difference between the steady and transient solution is 1.4%.
Results for the mesh convergence study is shown in Fig.24. The number of elements in increasing order corresponds to a pontoon face mesh size of 7·10−3m to 3·10−3m with steps of−10−3 m, respectively.
20 30 40 50 60 70 80 90 0.4 0.5 0.6 0.7 0.8 0.9
1 Steady state solutions Transient at flow time 200 s
Figure 23– Drag coefficient against the cut angles. The values have been scaled with drag
coefficient value for the 90◦cut angle. The value for the transient solution is also shown.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.22 1.225 1.23 1.235 1.24 1.245
Figure 24– Mesh convergence when varying the pontoon face mesh size. The number
of elements in increasing order corresponds to a pontoon face mesh size of 7· 10−3 m to
4.3
Calibration of magnetometer
The uncalibrated magnetometer data for all three planes can be seen in Fig.25. Using the obtained calibration constants, found in Appendix E, on the uncalibrated data, one will get three circles centered at the origin as Fig.26 shows.
-1000 -800 -600 -400 -200 0 200 400 600 -800 -600 -400 -200 0 200 i = x, j = y i = x, j = z i = y, j = z
Figure 25– Uncalibrated magnetometer data for each plane.
-600 -400 -200 0 200 400 600 -500 -400 -300 -200 -100 0 100 200 300 400 500 i = x, j = y i = x, j = z i = y, j = z
4.4
Current measurements
The current measurement for the 5 V supply showed a peak current of 0.4 A and the peak current for the DC motor rotating the RBR was 1.83 A. The final measurement of the pair of brushless motors can be seen in Fig.27. Fully charged batteries gives a 12 Ah capacity which are used for the two sets of motors. An estimate for the minimum run-time of the mobile reactor on a set of fully charged batteries can easily be obtained from these current measurements. As Fig.27 shows, using the base speed, which is using 15% of max power, should give a current value just below 1 A for the pair of brushless motors. To be on the safe side, lets estimate using the current value for 20% of max power which is 1.26 A. As the set of DC motors use 3.66 A together, a total current draw for all four motors is 4.92 A. Given a 12 Ah capacity, the mobile reactor have at least a run-time of 2.4 h or 144 minutes before it needs recharging. The current draw from the 5 V supply with a 2.6 Ah, is only 0.4 A. This battery will thus last around 6.5 h if it is fully charged.
0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5
Figure 27– Current measurement for the pair of brushless motors when varying the power
given to each motor.
4.5
Experimental test of autopilot
The path of the first autopilot test using the P controller, can be seen in Fig.28. The autopilot successfully passed 5 waypoints but had to be aborted since the route was poorly drawn. The last point, waypoint 6, was apparently placed on land thus giving the autopilot no chance of completing the route. The second test using the PI controller successfully completed the whole route, which is shown in Fig.29.
20.026 20.0262 20.0264 20.0266 20.0268 20.027 20.0272 64.0228 64.0229 64.023 64.0231 64.0232 64.0233 64.0234
Figure 28– Travel path for the autopilot using a P controller.
20.3032 20.3034 20.3036 20.3038 20.304 20.3042 20.3044 20.3046 20.3048 63.82075 63.8208 63.82085 63.8209 63.82095 63.821 63.82105 63.8211 63.82115 63.8212
4.6
MATLAB routine
To illustrate how a typical travel route can look like for the TSP solver and the brute-force zigzag method, the two algorithms have been given the same boundary points, with a minimum distance to waypoints of 9 m and maximum 3 m to the edge. The output travel path for the TSP solver can be seen in Fig.30 and the brute force zigzag method in Fig.31. 20.3142 20.3144 20.3146 20.3148 20.315 20.3152 20.3154 20.3156 20.3158 63.8171 63.8172 63.8173 63.8174 63.8175 63.8176
Figure 30– Travel path for a given boundary using the TSP solver method.
20.3142 20.3144 20.3146 20.3148 20.315 20.3152 20.3154 20.3156 20.3158 63.8171 63.8172 63.8173 63.8174 63.8175 63.8176
5
Discussion and conclusion
5.1
Mobile reactor
The final design of the mobile reactor was decided by considering the pros and cons of possible designs. The factors that were considered was the shape of the hull, material of the hull, kind of propulsion, placement of RBRs as well as the accessibility and cost of parts.
5.1.1 Hull
There are essentially two main categories of hulls that a surface vehicle can be created from. The first category is the monohull vehicles and the second one is the multi-hull vehicles. As the names suggests, the monohull vehicles consist of only one single piece of hull, like a classic row boat, while the multi-hull vehicles have at least two separate pieces. A common multi-hull vehicle is the catamaran (twin hull).
There are multiple reasons why a catamaran design was chosen for the mobile reactor. The first factor that heavily favors the chosen design is that the space between the two pontoons gives a natural location to place the RBRs and at the same time gives them protection from any external collisions. If the reactor would hit an obstacle in the front or side, the hull will take the hit and not the RBRs. The only way to get this kind of natural protection in a monohull is by drilling a hole in the bottom and this is obviously not ideal since there is a high risk of leakage. Catamarans are often used for unmanned surface vehicles because they provide greater stability, decreasing the risk of capsizing in rough waters and offers a greater payload capacity[24]. Even though the mobile reactor will not be operating in rough waters, greater stability and reduced risk of capsizing are vital qualities in order to achieve stable operation. Another benefit of using a catamaran design is that storing and transporting the vessel is considerably easier since the pontoons offers a plane surface.
5.1.2 Cut angle of pontoon
There was never any doubt that a smaller cut angle would give a smaller drag coefficient, as a better streamlined body should give a smaller Cd. As Fig.23 shows, the simulations
results does match the common belief. However, the interesting part is not the absolute decrease of Cd for smaller cut angles, but rather the relation between the two quantities.
We can see that the relation is not linear across the whole range and the cut angle needs to be quite small in order to see a large effect. Going to a 70◦ cut angle does not even decrease Cd 10%. The decision for the 35◦cut angle was based on the simulation results
but also on practical reasons. As the angle decreases, the total length of the pontoon needs to increase if we want the same load capacity. 35◦was also the smallest angle that could be cut with available tools. 35◦angle was a suitable choice from both an efficiency and practical perspective since it both offered a Cd decrease of almost 50% compared
procedure.
The expectation that the drag coefficient would reach a steady state proved to be a good assumption for the purpose of these simulations, as the difference between the steady state solution and transient solution was only 1.4%. As the discrepancy is so small, using all transient solutions would not have changed the decisions about the 35% cut angle, since it was not based on knowing the exact values of Cd. A larger cut angle would
only be justified if we had an exponential relation of some sort, thus using steady state simulations were a good approximation. The mesh convergence in Fig.24 also shows that even finer mesh would not give large deviations in the results. As going from 0.6·106to 1.6 ·106 mesh elements, where the latter is what Fig.23 is based on, does not have any major impact on Cd. Thus having an even finer mesh would also not change any decisions
taken, based on the simulation results. 5.1.3 Material and products
The hull is mainly created from PVC, a plastic known for its strength, durability and water resistance. Another great thing with PVC is that it is easily accessible and relatively cheap compared to other materials. The materials considered were either PVC or Aluminum. Aluminum is also relatively cheap, easily accessible and most of all, corrosion resistant. Aluminum is also a common material used in larger pontoon boats. The down-side of using Aluminum, and the reason why it was not used, is that the material is considerably harder to work with, compared to PVC. To obtain a complete hull, aluminum has to be welded tight, tools which are not easily accessible and a custom order would likely spend most of the project budget.
When developing a product such as the mobile reactor, which contains many different parts, there is a large probability that some of the products used in the assembly does not quite work as first intended. The mobile reactor is not an exception. Using a relay to turn the DC motors off and on is not the optimal choice, as it is not possible to control the RPM of the motors. Originally a dc motor chip (L298N) was used instead of a relay, where the RPM of the motors could be controlled. Unfortunately it turned out that the chip overheated and shut off even though the current was below the chip limit. Next, the stainless steel propeller shafts which was specified for marine purposes, was actually not fully stainless and not as water proof as first expected. Applying propeller grease helped with the water leak but if this holds for longer operations is still unknown. This is the entire purpose of the implemented water sensor, as it offered a way to check whether a leak had occurred or not. A more long term solution is to change the relays to a suitable chip that can withstand the current levels. An even better solution would be to change the DC motors to brushless motors since they are generally better suited for long term use. Changing the propeller shafts to something of higher quality is also a better long term solution. Unfortunately there was no time to make these changes within present project, but it could be resolved in future work.
5.1.4 Electronics
Considering the magnetometer data in Fig.25 and Fig.26, the reader might find it strange that the data does not only form an ellipse or circle, but that also there are some scattered data. This comes from the fact that we collect data in 3D space while the figures shows the projected data in 2D. If we instead only measured Mxand Mywhen the mobile reactor
was rotated in the x-y plane and only Myand Mzduring rotation in y-z plane and similarly
with the x-z plane, then the data would form three ellipses/circles with no scattered data. The scattered data does not affect the calibration in any negative way since the objective is to find the minimum and maximum values that each axis can read. The calibration procedure is quite tedious, but fortunately it only needs to be performed once, as long as any equipment is not moved relative to magnetometer. Moving or changing any equip-ment, especially magnetic materials such as the DC motors, will most likely change the surrounding distortions and a new calibration have to be made for the magnetometer to show correct heading.
One of the limiting factors with the mobile reactor is of course the battery time. With the current set of batteries, the mobile is able to run around approximately 144 minutes before recharging. What could be noted is that the measurement of the pair of brushless motors was made when the mobile reactor was fixed in space. This means that any effect that rotating RBRs might have on the measurement due to additional drag is not considered in the measurement. To find whether it has any effect, one would need to measure the current during a running operation. The estimate of 144 minutes also assumes that the full capacity of the batteries can be used with full efficiency, which is probably not the case. The easy solution for obtaining longer run-time is of course to add more batteries and also solar cells can be a suitable future implementation for longer run-time without the need to recharge.
5.2
Autopilot comparison
Comparing the travel path for P controller in Fig.28 with the PI controller in Fig.29, would directly result in the conclusion that the P controller performs better as the travel path is much smoother and precise. However, such a comparison would not be fair to the PI controller since the weather conditions were completely different. Both tests had similar water conditions, but the test for the P controller was conducted on a clear blue sky while the PI controller was put to the test on a very cloudy and foggy day. There are some different opinions whether clouds and fog actually affects the GPS signal, but since it was discovered that the mobile reactor lost the GPS signal completely during other tests the same day, it is safe to say that the PI controller did not have the best GPS signal. The test of the PI controller also used a very small coefficient ki. This means that the error
had to be quite large during a long time for the integrating part to have any noticeable effect on the control signal. The difference between the P and PI controller should thus not be that large, which further indicates that the weather conditions had a larger effect between the two tests than the choice of controller. Unfortunately, there was no time to better tune the PI controller. To give the PI controller a fighting chance, further testing should be made where different types of controllers are tested on the same course and
with the same weather conditions.
Theoretically a PI controller should be preferred over a P controller. If there is a lot of wind and waves forcing the mobile reactor in certain direction, a P controller could reach a state which produces a steady state heading which is not aligned to the waypoint. A problem which can be dealt with using a PI controller since the integrating term will increase the control signal if the error persists over a longer period of time. On the other hand, since the field of deployment is not an environment with heavy winds and waves, the P controller will likely work just fine. In any case, both tests validated that the autopilot can operate autonomously for a given route.
As the autopilot testing was made without any RBRs attached, one might wonder if adding them will have any effect. There has been some informal testing using an RBR attached and driving the mobile reactor in radio control mode. These informal tests hinted that the rotation of the RBRs had negligible effect on the steering of the mobile reactor, but as it added some additional resistance, the only noticeable effect was a lower forward speed compared to a mobile reactor without any RBR.
5.3
Future implementations
In addition to the potential improvements mentioned above, there are a few implemen-tations left to do. The solid phase inside the RBR will not last forever, meaning that the RBR will have to be exchanged from time to time. The mobile reactor is designed from the standpoint that this exchange should be made by an external docking station. This might involve a new design for the locking mechanism of the RBR for easier re-placement. Ideally the batteries should last until the RBR needs replacement, since both exchanges can be made at the same time for minimal downtime.
As this was the first version of the autopilot, there are some things that can be improved. Currently the autopilot does not have any way to detect obstacles, which might be useful in some applications. Obstacle detection can be achieved by using for instance either camera techniques or sonar sensors. If better precision of travel path is needed in future, it could be an idea to introduce some kind of filter for the sensor data. One filter commonly used with GPS and magnetometers sensors is the Kalman filter.
5.4
Assessment of goals
In this project four goals were set and here are comments on their assessment.
1. Construct a stable hull which allows for safe and stable operations in water con-ditions resembling an indoor pool environment.
As with any product, there is room for improvement. However, as the current mobile reactor successfully completed two autopilot tests with stable performance, the first goal can be classified as fulfilled.
2. Implement manual (radio controlled) and autonomous (GPS controlled) driving.
The second goal is also fulfilled as the mobile reactor is both operable using a radio control and autopilot.
3. Implement a routine for choosing travel route given an area of operation.
The implemented MATLAB routine gives the user the three ways of obtaining a route. The best method will be dependent on the given boundary and the users of the program will have to decide what method they want to use. The implemented program fulfills the third goal.
4. Be able to estimate of the time needed for the raft to process a given body of water.
The last goal was not fulfilled due to lack of time. Many things during the assembly of the mobile reactor took longer time than intended. Adding the time delay due to unexpected problems along the way, there was simply no time left for the last goal. Estimating the process time involves experimental testing using the mobile reactor. In future work this goal can be fulfilled by making experimental testing of the process time at different water scales and then finding a relation between the process time and water volume.
5.5
Conclusion
The developed mobile reactor proves the possibility to achieve stable operations using a twin-hull design and relatively cheap materials. With the new design and added func-tionality, such as autonomous driving, the mobile reactor has taken the next step towards a final product. As the mobile reactor is very modular in its design, it offers ways to implement future improvements and changes, without having to remake the whole prod-uct. Finally, even though only three out of four goals are fulfilled, all goals relating the construction and implementation of the mobile reactor are completed. This means that large scale water treatment now have a new tool at hand, namely the mobile reactor.
