Mt Introduction. 2. Governing gphysics. 3. Decomposition of resistance. 4. Similarity laws and scaling
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1 1. Introduction 2. Governing gphysics 3. Decomposition of resistance 4. Similarity laws and scaling Mt 527
2 Importance of proper power-speed prediction Resistance, prop. efficiency, power Wake field Experimental, empirical or numerical prediction Propeller design and cavitation
3 Understand the mechanisms for ship resistance and extrapolation to another scale. Understand the principles of ship propulsion (actuator disk, ideal efficiency) Master a first propeller p design capability based on systematic series Understand cavitation nuisance and have a Understand cavitation nuisance and have a first understanding of the principles.
4 Historic Perspective
5 Earliest model tests 1500 approx. - Leonardo da Vinci Tests on 3 different models with variations in fore- aft displacement distribution 1650 approx. Samual Fortrey Towing tests with small wooden models in tank 1770 approx. Pieter van Zwijndrecht Pauluszoon Towing tests with different waterline models 1871 First purpose built Tow Tank by Froude in Torquay (UK) 1873 Model tests by Bruno Tideman with naval cruiser Atjeh at the Rijkswerf in Amsterdam 1932 Opening of the Nederlandsch Scheepsbouwkundig Proefstation (NSP) in Wageningen (currently MARIN) But how to scale these models and tests? William Froude 1868 Decomposition of total resistance R T =R F +R R? R F =flat plate frictional resistance R R =residuary resistance 1883 Notion of Reynolds number and scaling
6 1687 Newton s Pilosophiae Naturalis Principia Mathematica 1752 d Alembert published what is now called D Alembert s paradox ado in response se of a contest organized by the French Academie des Sciences 1757 Euler (Swiss mathematician) ti i published an important equation governing an inviscid flow Development Navier-Stokes equations
7 Underlying Principles
8 What are the principles of the fluid dynamic equations The conservation laws
9 The Resistance Breakdown
10 Source: ITTC 1972 Res. Committee
11
12 On flow phenomena
13 u y sheer stress [N/m2]: u velocity U (m/s) length scale L (m) viscosity (Pa s) (kg/ms) density d (kg/m3) kinematic viscosity (m2/s) [ Pa sec] [ kg / m ] 3 Reynolds: small => viscosity dominated => viscous flow UL/ (-) high => inertia dominated => potential flow
14 C f (Re) = Rt / 0.5ρU 2 Sis not a constant t C f decreases with Re
15 BL thickness, 99 is difficult to measure => integral measurements displacement thickness momentum thickness
16 Transition: Re x,cr 10 5
17
18 Exception where turbulence reduces the drag!! => golf ball => suits for ice skaters
19
20 Reduction of the wake >l t l => lower momentum loss => lower resistance
21 dp/dx > 0: favourable pressure gradient (bow) Stabilises BL dp/dx < 0; adverse pressure gradient (stern) destabilises BL
22 Potential ti flow; no friction, no pressure gradient => No drag High Re; limit 0; no friction?? Experiments: always finite drag => D'Alembert paradox
23
24 From flow over plate and cylinder: pressure => BL growth => friction friction => separation => pressure Froude hypothesis: For streamlined bodies (small dp/dx) without flow separation assume that pressure (form) drag and friction drag are independent => Application on ship design: Form factor and flat plate resistance
25 1. Introduction read 2. Governing equations : understand, need not be reproduced : BCs: Be able to reproduce physical origin of bc s 3. Similarity reproduce similarity numbers if N-S Seq. isgiven reproduce consequences of similarity requirements 4. Decomposition of resistance Reproduce Understand appendix from BB Notes on Resistance Breakdown ITTC/Paffett 1972
26 Derivation of Rn, En, Fn, Wn from N-S eq. and bc s Rn-Fn dilemma
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