1 tmr4225 marine operations, 2009.01.27 lecture content: –linear submarine/auv motion equations...
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TMR4225 Marine Operations, 2009.01.27
• Lecture content:– Linear submarine/AUV motion equations
• Dynamic stability (stick-fixed stability)
• Neutral point
• Critical point
– AUV hydrodynamics – Hugin operational experience
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Linear motion equations
• Linear equations can only be used when– The vehicle is dynamically stable for motions in horisontal and
vertical planes
– The motion is described as small perturbations around a stable motion, either horisontally or vertically
– Small deflections of control planes (rudders)
– For axi-symmetric bodies the 6DOF equations can be split in two sets of equations
• 2 DOF for coupled heave and pitch
• 3 DOF for sway, yaw and roll
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Dynamic stability
• Characteristic equation for linear coupled heave - pitch motion:– ( A*D**3 + B*D**2 + C*D + E) θ = 0
• Dynamic stability criteria is:– A > 0, B > 0 , BC – AE > 0 and E>0
• Found by using Routh’s method
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Roots of stability for a submarine
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Speed variation of damping ratio for a submarine
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Transient response for vertical motion – variation of the damping ratio
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Neutral point position (from Hoerner ”Fluid Dynamic Lift”)
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Critical point – variation with forward speed
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Dynamic stability (cont)
• For horizontal motion the equation (2.15) can be used if roll motion is neglected
• The result is a set of two linear differential equations with constant coefficients
• Transform these equations to a second order equation for yaw speed
• Check if the roots of the characteristic equation have negative real parts
• If so, the vehicle is dynamically stable for horizontal motion
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Traditional approach
• Manoeuvring problem– Calm water
– Large vessel motions in the horizontal plane only
– Problem formulated in a body-fixed coordinate system
• Seakeeping problem– Incident waves
– Focus on vertical motions (heave and pitch)
– Body motions assumed small about mean position of vessel
– Problem formulated in a coordinate system fixed with respect to the mean position of vessel
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New formulation including manoeuvring in waves
• The asymptotic solution of the sea keeping formulation when ω -> 0 will NOT give the traditional manoeuvring equations
• Seakeeping model will also give time-independent forces
• Use of rudder and propulsive forces will introduce dynamic forces in the sea keeping model
Inconsistent behaviour if hydrodynamic model is based on traditional approach
• The traditional maneuvering equations must be obtained by setting the frequency to zero
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The different reference frames
• The north-east-down reference frame (NED frame)– Main coordinate system of ship simulator– Wave/wind/current environment
• The hydrodynamic reference frame (HYDRO frame)– Fixed with respect to mean position of ship– Seakeeping formulation
• The body-fixed reference frame (BODY frame)– Manoeuvring formulation
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Unified formulation – Development steps
• Establish transformations between the BODY and NED frames
• Establish transformations between the BODY and HYDRO frames
• Formulate unified formulation in the BODY frame in the frequency-domain (ie transform the sea keeping formulation from the HYDRO frame to the BODY frame).
• Formulate the unified formulation in the time-domain
• Calculate 2D hydrodynamic coefficients and exciting forces
• Calculate frequency dependent added mass and damping coefficients in unified formulation
• Calculate retardation functions
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AUV overview
• AUV definition:– A total autonomous vehicle which carries its own power and does
not receive control signals from an operator during a mission
• UUV definition:– A untethered power autonomous underwater vehicle which
receives control signals from an operator
– HUGIN is an example of an UUV with an hydroacoustic link
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AUV/UUV operational goals
• Military missions– Reconnaissance
– Mine hunting
– Mine destruction
• Offshore oil and gas related missions– Sea bed inspection
– Pipe line inspection
• Sea space and sea bed exploration and mapping– Mineral deposits on sea floor
– Observation and sampling
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Generic axis system for AUV
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Vector definitions
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6 DOF matrix equation for AUV motion
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Mass matrix
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HUGIN history
• AUV demo (1992-3)– Diameter: 0.766 m Length: 3.62/4.29 m
– Displacement: 1.00 m**3
• HUGIN I & II (1995-6)– Diameter: 0.80 m Length: 4.8 m
– Displacement: 1.25 m**3
• HUGIN 3000C&C and 3000CG (1999-2003)– Diameter: 1.00 m Length: 5.3 m
– Displacement: 2.43 m**3
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HUGIN family
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Initial HUGIN design
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Hugin UUV
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Forebody pressure drag (Hoerner)
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Resistance coefficient – aft body
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Drag coeffient variation with slenderness ratio
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Radius effect on drag for 2D bodies (Hoerner)
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Drag measurement – Hugin prototype
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Panels for added mass calculation
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Added mass matrix for HUGIN prototype
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Stinger for AUV testing in cavitation tunnel
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Heave force variation with pitch angle
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Offshore oil and gas UUV scenario
• Ormen Lange sea bed mapping for best pipeline track
• Norsk Hydro selected to use the Hugin vehicle
• Hugin is a Norwegian designed and manufactured vehicle
• Waterdepth up to 800 meters
• Rough sea floor, peaks are 30 – 40 meter high
• Height control system developed for Hugin to ensure quality of acoustic data
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Phases of an AUV/UUV mission
• Pre launch• Launching• Penetration of wave surface (splash zone)• Transit to work space• Entering work space, homing in on work task• Completing work task• Leaving work space• Transit to surface/Moving to next work space• Penetration of surface• Hook-up, lifting, securing on deck
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AUV – Theoretical models
• Potential theory– Deeply submerged, strip theory
– VERES can be used to calculate
• Heave and sway added mass
• Pitch and yaw added moment of inertia
– VERES can not be used to calculate
• Surge added mass
• Roll added moment of inertia
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AUV- Theoretical models
• Viscous models
• Solving the Navier Stokes equations– Small Reynolds numbers (< 1000) : DNS
– Medium Reynolds numbers (< 10**5) : LES – Large Eddy Simulation
– High Reynolds numbers (> 10**5) : RANS – Reynolds Average
Navier Stokes
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AUV – Theoretical models
• 3D potential theory for zero speed - WAMIT– All added mass coefficients
– All added moment of inertia coefficients
– Linear damping coefficient due to wave generation
• Important for motion close to the free surface
• More WAMIT information– http://www.wamit.com
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NTNU/Marine Technology available tools:
• 2 commercial codes– Fluent
– CFX
• In-house research tools of LES and RANS type
• More info: Contact Prof. Bjørnar Pettersen
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AUV – Experimental techniques
• Submerged resistance and propulsion tests– Towing tank
– Cavitations tunnel
• Submerged Planar Motion Mechanism tests– Towing tank
• Oblique towing test– Towing tank
• Lift and drag test, body and control planes– Cavitations tunnel
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AUV – Experimental techniques
• Free sailing tests– Towing tank
– Ocean basin
– Lakes
– Coastal waters
• Free oscillation tests/ascending test– Water pool/ Diver training pool
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NTNU/MARINTEK HUGIN involvement
• AUV demo (1992-3)– Model test in cavitation tunnel, open and closed model, 2 tail
sections (w/wo control planes)• Resistance, U = {3,10} m/s
• Linear damping coefficients for sway, yaw, heave and pitch, yaw/trim angles {-10, 10} degrees
– 3D potential flow calculation • Added mass added moment of intertia
– Changes in damping and control forces due to modification of rudders
– Student project thesis
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NTNU/MARINTEK HUGIN involvement
• HUGIN 3000– Resistance tests, w/wo sensors
• Model scale 1:4
• Max model speed 11.5 m/s
• Equivalent full scale speed?
– Findings• Smooth model had a slightly reduced drag coefficient for increasing
Reynolds number
• Model with sensors had a slightly increased drag coefficient for increasing Reynolds numbers
• Sensor model had some 30% increased resistance
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HUGIN 1000 layout
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Hugin navigation system
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HUGIN navigation system - items
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HUGIN communication system
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HUGIN sub system overview
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HUGIN information
• New vessels have been ordered late 2004 and 2005– One delivery will be qualified for working to 4500 m waterdepth
• New instrumentation is being developed for use as a tool for measuring biomass in the water column
• Minecounter version HUGIN 1000 has been tested by Royal Norwegian Navy
• More Hugin information: see Kongsberg homepage for link
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HUGIN field experience
• Offshore qualification sea trials (1997)
• Åsgard Gas Transport Pipeline route survey (1997)
• Pipeline pre-engineering survey (subsea condensate pipeline between shore based process plants at Sture and Mongstad) (1998)
• Environmental monitoring – coral reef survey (1998)
• Fishery research – reducing noise level from survey tools (1999)
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HUGIN field experience• Mine countermeasures research (1998-9)• Ormen Lange pipeline route survey (2000)• Gulf of Mexico, deepwater pipeline route survey (2001 ->)• Raven, West Nile Delta, Egypt, area of 1000 km**2 was
surveyed late 2005 by Fugro Survey– Sites for subsea facilities– Route selection for flowlines, pipelines & umbilicals– Detect and delineate all geo-hazards that may have an impact on
facilities installation or well drilling– Survey area water depth: 16 – 1089 m (AUV used for H > 75 m)– Line spacing of 150 m and orthogonal tie-lines at 1000 m intervals– Line kilometers surveyed by AUV: 6750 km – Distance to seabed (Flying height): 30-35 m– Operational speed: 3.6 knots
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Fugro survey pictures
http://www.fugrosurvey.co.uk/
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Actual HUGIN problems
• Inspection and intervention tasks– Adding thrusters to increase low speed manoeuvrability for
sinspection and intervention tasks• Types, positions, control algorithms
– Stabilizing the vehicle orientation by use of spinning wheels (gyros)
• Reduce the need for thrusters and power consumption for these types of tasks
– Docking on a subsea installation• Guideposts
• Active docking devices on subsea structure (robotic arm as on space shuttle for capture of satelittes)
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Actual HUGIN problems
• Roll stabilization of HUGIN 1000– Low metacentric height– 4 independent rudders – PI type regulator with low gain, decoupled from other regulators
(heave – pitch – depth, sway – yaw, surge)– Task: Keep roll angle small ( -> 0) by active control of the four
independent rudders• Reduce the need for thrusters and power consumption for these types of
tasks
– Docking on a subsea installation• Guideposts
• Active docking devices on subsea structure (robotic arm as on space shuttle for capture of satelittes)
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Future system design requirements
• Launching/ pick-up operations up to Hs = 5 m when ship is advancing at 3-4 knots in head seas
• Increasing water depth capability
• Increased power capability– Operational speed 3- 4.5 knots
– Mission length 3- 4 days
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Hugin deployment video
• Video can be downloaded from Kongsberg homepage