MEC-E2001 Ship Hydrodynamics Prof. Z. Zong zhi.zong@aalto.fi Room 213a, K3, Puumiehenkuja 5A, 02510 Espoo
Teacher: Prof. Z. Zong, zhi.zong@aalto.fi Room 213a, K3, Puumiehenkuja 5A, 02510 Espoo Teaching assistant: Ms Yan Dongni, Room 213a, K3, Puumiehenkuja 5A, 02510 Espoo Lecture: 31.10-05.12, 2017, 8:15-10, Tue & Thur, R008/202 Exercises: 02.11-07.12,2017, 10:15-12:00 Thur, R008/202 Model tests at VTT (20.11.2017,21.11.2017 & 22.11.2017) Examinations: 12.12,2017, 9:00-12:00 Tue, R008/202
a) Frictional resistance b) Viscous pressure resistance c) Wave-making resistance d) Eddy resistance e) Appendix resistance f) Air resistance g) Added resistance and others 1. Types of Resistances Phenomena descriptions
Topic: Types of Resistance After this part, you can explain How many types of resistances. How each resistance component is generated How to describe the dominant resistance component in dimensionless numbers. Resistance category. Additional reading Matusiak, Jerzy (2008). Short Introduction to Ship Resistance and Propulsion. Section 2.6. (English lecture notes in Noppa) Matusiak, Jerzy (2010). Laivan kulkuvastus, M-289, Section 2.4. and Chapter 4 (Finnish lecture notes in Noppa) Lecture- ship hydrodynamics 4
General When a ship moves forward through the water at a constant velocity V, it experiences a resistance or drag. Resistance or drag is the retarding force acting on a body that moves through a fluid. It acts opposite to the relative motion of the body. Buoyancy Resistance (drag) Thrust Weight 5
(a) Frictional resistance R f Even plate experiences resistance as fluid flows over it. Arising from viscosity It gives rise to drag force to any object moving through a fluid or equivalently, when a fluid flows past an object. 6
(a) Frictional resistance R f Boundary layer and main flow The flow can be divided into two regions (Prandtl, 1875-1953): Boundary layer: The region near the wall where the movement of the flow is controlled by the frictional resistance Main flow: The other region outside the above is not affected by the friction (and can be assumed to be ideal fluid flow). Lecture- ship hydrodynamics 7
(a) Frictional resistance R f Flow in a boundary layer Laminar flow The fluid travels smoothly. Flow properties (e.g. velocity, pressure) at each point in the fluid remain constant. Turbulent flow Unsteady. The fluid undergoes irregular fluctuations and mixing. Formation of vortices. Where does the transition occur? If smooth surface, around Re = 0.5 10 cr 6 Depends on the surface roughness. Lecture- ship hydrodynamics 8
(a) Frictional resistance R f Boundary layer thickness δ: laminar vs turbulence Laminar Turbulence d 5.853 = n x d 0.375 Re 0.2 x Re x = = x V x Re x 2 4 u y æ yö æ yö = 2-2ç + ç V d èd ø èd ø u V æ yö = ç èd ø 1/7 Lecture- ship hydrodynamics 9
(a) Frictional resistance R f Boundary layer thickness δ: laminar vs turbulence The boundary layer thickness is smaller in laminar than in turbulent flow. Lecture- ship hydrodynamics 10
(a) Frictional resistance R f Local shear stress at wall can be expressed roughly du t = 0 µ 2µ y = d V ( x) d = x 5.853 Re x and the resistance per unit width of plate of length L D L = òt 0dx= 0 0.664r Re 2 V L Frictional Resistance Coefficient (laminar): L Re L = Frictional Resistance Coefficient (turbulent): U L n C C f f º D 1 2 ru 2 L = 1.33 Re D º = 2 2 0.2 1 ru L ReL Lecture- ship hydrodynamics L 0.074 11
(a) Frictional resistance R f Frictional coefficient in laminar and turbulent flow They seldom used in ship hydrodynamics Lecture- ship hydrodynamics 12
(a) Frictional resistance R f Example Estimate Full scale: Ratio of the boundary layer thickness at midship and the length of the ship: δ S /L S Model scale: Ratio of the boundary layer thickness at midship and the length of the model: δ M /L M Case parameters Ship: L S = 100m, V S = 20kn OR your own ship. Model: L M = 4m. Lecture- ship hydrodynamics 13
(b) Viscous Pressure Resistance R vp 14
(b) Viscous Pressure Resistance R vp Pressure distribution is not fore-aft symmetric, resulting in pressure difference. Its integration along the surface is viscous pressure resistance Lecture- ship hydrodynamics 15
(b) Viscous Pressure Resistance R vp Lecture- ship hydrodynamics 16
(b) Viscous Pressure Resistance R vp 17
(b) Viscous Pressure Resistance R vp 18
(c) Wave-making resistance R W Widely exists behind ship and even a duck. Observable long behind. First studied by Load Kelvin in 1860s. 19
(c) Wave-making resistance R W Diverging waves Wave crest Transverse waves diverging waves on each side of the ship with their crests inclined at an angle to the direction of motion transverse waves with curved crests intersecting the centreline at right angles. 20
(c) Wave-making resistance R W The angle of the divergent waves to the centreline is 1 3 0 arcsin» 19 28 The waves move with the ship so the length of the transverse waves must correspond to this speed w = gk 2 l = 2 pv / g 2 p l =,V = k l T 21
(c) Wave-making resistance R W u There is no such thing as free lunch. u Waves are generated by consuming energy. Consumed energy is resistance which must be opposed by the propulsor if the ship is not to slow down. RW = 1 rga 4 2 u A submerged body near the surface will also cause waves and they become negligible at depths a little over half the body length. 22
(c) Wave-making resistance R W Kelvin derived single moving pressure point (1869) 1 1 G( x -x, y -h, z -z ) = - + 4pr 4p 2 k + k sec q 0 ( z+ e 2 k - k sec q 0 p / 2 {- ik[ ( x -x)cosq + ( y -h) q ]} Re ò ò exp sin 2 k z ) -p / 2 0 dkdq 23
(c) Wave-making resistance R W Mitchell (1898) thin ship theory R = P 2rg 6 pv 4 p / 2 ò -p / 2 ( P 2 + Q iq = - ik cosq 2 1 0 L / 2 + ò ò 5 )sec qdq -T -L / 2 f exp x Bow and stern are important B/L controls resistance [ kz + ikx cosq ] dq 24
(d) Eddy resistance u Where there are rapid changes of section the flow breaks away from the hull and eddies are created. u Examples of eddy creators: Transom stern, stern frames, appendages such as the bilge keels, rudders and so on. 25
(e) Appendix resistance u Appendages include rudders, bilge keels, shaft brackets and bossings, and stabilizers. u Appendage resistance can be obtained by testing appendages separately and scaling to the ship. 26
(e) Appendix resistance 27
(f) Air resistance R AA The ship actually moves at the same time through two fluids, water and air, with widely different density. While the lower part of the hull is moving through water, the upper part is moving through air. Like moving in the water, the upper part of the ship moving in the air is also subject to the same types of forces (dynamic pressures and tangential stresses). Because r a << r w, the air resistance is usually much smaller than the water resistance, except for those aerostatic support of hydrodynamic support crafts. 28
(f) Air resistance R AA Work at the National Physical Laboratory (Shearer and Lynn, 1959-1960) introduced the concept of an ahead resistance coefficient (ARC) defined by: ARC = fore and aft component of wind resistance 1 2 R T 2 rv A Where V A is the relative velocity and A C is the transverse cross section area. 29
(h) Added resistance and others Resistance in waves Resistance in restricted waters Wind Two ships are close 30
Summary Wave-making resistancer F Total resistance Total resistance Viscous resistancer E Frictional resistancer G Residuary resistancer I Viscous pressure resistancer HE Frictional resistancer G Viscous pressure resistancer HE Wave-making resistancer F Hull resistance Total resistance in calm water Appendage resistance Note: water resistance is the dominant factor in determining the speed. 31
Summary 32
Summary Example: Importance of different components Tanker Fn=0.15 Container Fn=0.24 Trawler Fn=0.34 Hydroplane Fn=1.5 Friction (flat plate) Effectof theform Effect ofsurface roughness Waveresistance Air resistance Resistance due to appendages
34