Design for the Ocean EnvironmentSome Major ConsiderationsWave FieldsLinear Wave Theory (deepwater)Statistics of Extreme WavesForces in steady flowConcept of Drag, Lift, Moment (2D)Typical Drag Coefficients (frontal area)Recommended ReferencesMassachusetts Institute of Technology 12.097Design for the Ocean EnvironmentMassachusetts Institute of Technology 12.097Some Major Considerations• Hydrostatic pressure• Heat dissipation in housings•Waves• Forces on bodies in steady flow• But don’t forget: wind and rain, corrosion, biofouling, material fatigue, creep, chemical breakdown, human safety, regulations, etc.Massachusetts Institute of Technology 12.097Coefficient of thermal conductivity, W m / m2 oKYoung’s Modulus,PascalsUltimateStrength, PascalsDensity, kg/m3Steel 200e9 550e6 4400 8000Aluminum 70e9 480e6 22000 2700Titanium 100e9 1400e6 1500 4900Glass 70e9 <35000e6(compression!)100 2600ABS Plastic 1.3e9 34e6 LOW ~1100Mineral oil - 17 ~900Water 2.3e9 - 60 1000Massachusetts Institute of Technology 12.097Wave FieldsDefinition:SeaState Height (ft) Period (s) Wind (knots)2 1 7 93 3 8 144 6 9 195 11 10 246 16 12 377 25 15 51Distribution:30% of world oceans are at 0-1m height41% 1-2m 17% 2-3m6% 3-4m2% 4-5mWave height H1/3Significant wave: Average of one-third highest wavesWave fields depend on storms, fetch, topographyMassachusetts Institute of Technology 12.097Linear Wave Theory (deepwater)Wave elevation:η = ηcos( ω t – k x ) where η is amplitude ω is frequency in rad/s : period T = 2π/ωk is wavenumber in rad/m : wavelength λ = 2π/kDispersion Relation: k = ω2/ gWave speed: V = g / ωParticle velocities: u = k ηV e-kzcos ( ω t – k x)w = k η V e-kzsin (ω t – k x) where z is depthFluctuating pressure: p = ρ ηg e-kzcos ( ω t – k x )ηVMassachusetts Institute of Technology 12.097Statistics of Extreme Waves• Average of one-third highest waves is significant wave height Hsigor H1/3= 2 η1/3 • An observer will usually report H1/3•H1/10 = 1.27 * Hsig• Expected maxima: N = 100; 1.62 * H1/3N = 1000 ; 1.92 * H1/3N = 10000 ; 2.22 * H1/3Massachusetts Institute of Technology 12.097Forces in steady flow• Streamlined vs. Bluff Bodies– Bluff: Cylinders, blocks, higher drag, lower lift, large-scale separation and wake– Streamlined: airplanes and ship hulls, Lower drag but higher lift, avoids separation to minimize wake– Tradeoff in Directional Stability of the body: • A fully streamlined fuselage/fairing is unstable.• Drag aft adds stability, e.g., a bullet• Wings aft add stability, e.g., fins, stabilizers• Wings forward decrease stability, but improve maneuverability.• Turbulent vs. Laminar flow• High- vs. low-speed flowMassachusetts Institute of Technology 12.097Concept of Drag, Lift, Moment (2D)Flow ULift (normal to the flow)Drag (parallel to the flow)FrMoment = r X F depends on location of body frame!body frameTypical nondimensionalization:Drag = ½ ρ U2A Cd, where A is (typically) frontal area or wetted areaLift = ½ ρ U2A Cl, where A is usually a planform areaMoment = ½ ρ U2DL2Cm, where L is characteristic body length, and D ischaracteristic width (or diameter)Center of ForceMassachusetts Institute of Technology 12.097Typical Drag Coefficients (frontal area)• Square cylinder section 2.0• Diamond cylinder section 1.6• Thin rect. plate AR=1 1.1•AR=201.5•AR>>12.0• Circular cylinder section 1.1• Circular cylinder end on 1.0• 1920 Automobile 0.9• Volkswagon Bus 0.42• Modern Automobile < 0.3• MIT Solar Car?Potter & Foss (1982)Massachusetts Institute of Technology 12.097Recommended References• Fluid-Dynamic Lift. S.F. Hoerner, 1975, Hoerner Fluid Dynamics, Bakersfield, CA.• Principles of Naval Architecture, Volume III (Motions in Waves and Controllability), E.V. Lewis, ed., 1989, SNAME, Jersey City, NJ.• Fluid Mechanics, M.C. Potter and J.F. Foss, 1982, Great Lakes Press, Okemo, MI.• Theory of Flight, R. von Mises, 1945, Dover, New York.• http://naca.larc.nasa.gov/: NACA reports on bodies and