TS 4001: Lecture Summary 4 Resistance
Ship Resistance Very complex problem: Viscous effects. Free surface effects. Can only be solved by a combination of: Theoretical methods. Phenomenological methods. Experiments. Must predict resistance to select propulsion plant. 20 February 2002 Resistance 2
Speed-Power Trends EHP = (Resistance) x (Speed) For the horizontal axis: V in knots, L in feet. 20 February 2002 Resistance 3
Froude 1877 Ships make waves. Waves require energy. Energy is spent from the ship s propulsion plant. Therefore, waves = resistance. Test with models. But, that s only half the problem how about fluid friction? Unfortunately, viscous fluids were unknown to Froude. So, he tested with waveless models wooden planks. 20 February 2002 Resistance 4
Froude s Early Sketch 20 February 2002 Resistance 5
Sources of Resistance. Since ship resistance is such a complex problem, we have to break it down. To understand where it comes from, we have to understand the principal types of fluid flow. Look at a submerged body first, then bring in the free surface. 20 February 2002 Resistance 6
Fluid Flow - Submerged Examples of fluid flow for a submerged body (no waves): D Alambert s paradox 20 February 2002 Resistance 7
Fluid Flow - Surface 20 February 2002 Resistance 8
Types of Fluid Flow Potential flow. Viscous flow. Wavemaking. Flow separation. Circulation/Vortex motion. Cavitation. Hydrofoil flow. Elastic/Compressible flow. 20 February 2002 Resistance 9
Potential Flow Ideal, non-viscous or frictionless, streamline flow. Unbroken streamlines whose journey is made with no friction. Many applications: Wave making. Bernoulli law. 20 February 2002 Resistance 10
Viscous Flow Real, frictional flow. Attachment of innermost fluid particles to surface of body. Resistance to shear offered by moving particles in adjacent layers. Newtonian fluids. No-slip boundary condition. Boundary layer. 20 February 2002 Resistance 11
Wavemaking Occurs at the interface of two non-mixing liquids. Free surface is disturbed by oscillatory movements giving rise in propagating waves. Energy carried away by the waves constitutes the wave making resistance. Not to be confused with resistance in waves. Gravity plays a very important role. Both surface and sub-surface waves. 20 February 2002 Resistance 12
Flow Separation Occurs when streamlines are prevented from following contours of body. Vortices (or eddies) with circulatory motion and reverse flow are formed after separation. Important for resistance, but also for wake and propeller induced vibration. 20 February 2002 Resistance 13
Circulation/Vortex Motion Circulatory motion of fluid about an axis, in planes perpendicular to that axis. Solid body may surround axis, or gas pocket may enter on it. Forming a core around which the coil of circulatory motion takes place. 20 February 2002 Resistance 14
Cavitation Formation of bubbles, voids, or cavities alongside or behind a body moving in a fluid. Occurs when fluid pressure at a point on the body is reduced to vapor pressure of fluid. Will study it in more detail in the next set. 20 February 2002 Resistance 15
Hydrofoil Flow Combination of two or more flows. Relative motion of body and fluid develops drag and lift forces on the body at right angles to the direction of relative motion. Very important in special hull forms and in maneuvering and motion control (later). 20 February 2002 Resistance 16
Elastic Flow Traveling pressure Wave phenomenon. Arises from elasticity of fluid. Formation of shock pressure waves radiating at high speeds from exciting sources. Shock and vibration problem. 20 February 2002 Resistance 17
Conclusions Ship resistance is caused by many different fluid flow phenomena. These interact and combine in complex ways. Theoretical methods have not yet been developed to the point where model tests are not needed. 20 February 2002 Resistance 18
Resistance Source Summary Friction: dominant at low speeds, function of wetted surface area, speed, and roughness. Wavemaking: dominant at higher speeds, function of hull form and speed, part of residual resistance. Eddy/Form: result of pressure difference, part of residual resistance. Air/Appendage: not always designed for, can be significant. 20 February 2002 Resistance 19
Resistance Breakdown Different fluid flows generate different resistance components. This decomposition has some physical grounds and is used simply because it is convenient. Study the major resistance components separately. Then find a way to put them together. 20 February 2002 Resistance 20
Frictional Resistance Also known as viscous resistance. Aft acting force to set fluid within the boundary layer in motion. Depends on wetted surface of body, not its geometry. Zero for an ideal fluid. 20 February 2002 Resistance 21
Wavemaking Resistance Part of residuary resistance. Energy expended to produce waves is a measure of the work done by the ship on water. Nonzero even for an ideal fluid. Directly related to wavemaking by the body. Related to hull geometry. 20 February 2002 Resistance 22
Separation Resistance Also known as Form Drag. Part of residuary resistance. Occurs when fluid flow separates from hull, especially near the stern. (Residuary) = (Wavemaking) + (Separation) (Residuary) = (Total) - (Frictional) 20 February 2002 Resistance 23
Appendage Resistance Very difficult to predict and scale up: Vastly different scale from ship. Many causes: Eddy making resistance: Inability of water to flow in smooth streamlines around abrupt discontinuities; flow breaks clear and reverses; eddies fill in the void. Frictional resistance. Cavitation. Usually dealt with as a single number, either a total for all appendages, or each individual appendage. 20 February 2002 Resistance 24
Typical Appendage Resistance TYPE OF SHIP V L 0.7 1.00 1.6 Large, fast, 4 propellers 10-16% 10-16% - Small, fast, 2 propellers 20-30% 17-25% 10-15% Small, medium speed, 2 propellers 12-30% 10-23% - Large, medium speed, 2 propellers 8-14% 8-14% - All single propeller ships 2-5% 2-5% - V L : V in k n o ts, L in feet. 20 February 2002 Resistance 25
Air Resistance Consists of both frictional and eddy-making resistances caused by relative flow of air around above water part of the ship. Usually not designed for, but can be a major component in certain cases. Depends on air density, relative wind speed, projected area of above water part of the ship, and some resistance coefficient. Wind tunnel tests can be used to evaluate the air resistance coefficient. 20 February 2002 Resistance 26
Total (Total Resistance) = (Frictional Resistance) + (Residuary Resistance) + (Appendage Resistance) (1) + (Air Resistance) (1) + (Correlation Allowance) (2) (1) : If available. (2) : To patch things up. 20 February 2002 Resistance 27
Correlation Allowance All extrapolation methods require an adjustment to achieve correct correlation between model and ship. Determined by comparing full scale ship trials to previous model test results. Must be known in advance. Decreases with increasing ship length. 20 February 2002 Resistance 28
Typical Speed Profile Resistance (lbs) / Displacement (tons) Typical Resistance Characteristics of Displacement Vessels Ship is climbing its own bow wave Wavemaking resistance dominates at high speeds Speed/Length Ratio 20 February 2002 Resistance 29
Summary: Resistance Components Frictional Equivalent to resistance of flat plate being towed Form (Eddy/Separation) Energy lost in the formation of eddies caused by flow separation Wave Energy lost in the making and breaking of waves Appendage Air Added resistance of bilge keels, struts, shafts, rudders, and propellers Drag associated with superstructure and hull above the waterline Correlation Allowance Accounts for hull roughness and scaling differences between model and ship (Typically runs from 0.0004 to 0.0005) 20 February 2002 Resistance 30
Sources of Information Theoretical Calculations: Solution of the complete problem (Navier-Stokes with a free surface at high fluid speeds) is not yet practical. Wavemaking can be predicted relatively well, frictional not so. Tests: Full scale would be best but is of course not practical. Have to do model scale and then extrapolate. Preliminary: Regression analyses of earlier ship data. Standard series. 20 February 2002 Resistance 31
The Main Problem How do we extrapolate from model scale to full scale. How to scale up dimensions, velocities, and forces from model to full scale ship? In other words, how do we go 20 February 2002 Resistance 32
from this 20 February 2002 Resistance 33
to this. 20 February 2002 Resistance 34
Dynamic Similarity Consider two geometrically similar ships. How do we scale their resistance properties? Flows must be similar. Resistance depends on: Length, Water density, Kinematic viscosity, Ship speed, Acceleration of gravity, 20 February 2002 Resistance 35
Dimensional Analysis Assume: For this to be dimensionally correct: Solving: 20 February 2002 Resistance 36
The Resistance Equation Therefore: Since we have geometrically similar bodies: Therefore, we can write: 20 February 2002 Resistance 37
Resistance Coefficient The resistance coefficient is a function of the Reynolds number and the Froude number 20 February 2002 Resistance 38
Conclusions The two important parameters in ship resistance are: The Reynolds number, which physically represents viscous effects, and The Froude number, which represents wavemaking. Two geometrically similar hull forms (geosims) will have the same wave resistance coefficient if and only if they have the same Reynolds number and Froude number. How do we achieve this? 20 February 2002 Resistance 39
Resistance Calculations Want to find: (Re, Fn) If subscript s corresponds to ship and m to model we must have: ( C ) = ( C ) For that we need: V (Re) m = (Re) s or = V and R s R m C R L L m s s s m m 1/2 1/2 V m g m L m (Fn) m = (Fn) s or = Vs gs Ls ν ν 20 February 2002 Resistance 40
Is this possible? Pick a reasonable model/ship ratio L / L = 1/100 Then the previous requirements are: 1/2 Vm ν s Vm 1 g m = 100 and = Vs ν m Vs 10 gs In order to satisfy both we must either: (a) perform the experiments on a space station with adjustable orbit and adjustable g, or (b) invent an exotic fluid with kinematic viscosity one thousandth that of seawater. Unfortunately, none of these options is feasible. m s 20 February 2002 Resistance 41
So which one to choose? So we can't satisfy both both Re and Fn scaling simultaneously. Which one to choose? Call the ship/model ratio L / L = λ ( 1). Then we either satisfy s m This is for the same fluid for ship and model. Since λ ( 1), Re scaling is highly impractical. Fn scaling is all we can do. 20 February 2002 Resistance 42
Froude s Hypothesis So the problem is how to get (C R ) s from measurements of (C R ) m assuming Fn scaling only. Strictly speaking, since C R is a function of both Re and Fn, this is not possible. Froude s hypothesis is: C F is the frictional resistance coefficient and this is a function of Re only (assuming that the extra friction due to the waves generated by the ship is small). CW is the wavemaking resistance coefficient and this is a function of Fn only. C FORM is the form drag (separation resistance) and we assume that it is a function of hull geometry only. 20 February 2002 Resistance 43
Froude s Method Froude was able to verify this experimentally by pulling wooden planks down Thames and in his basement! 20 February 2002 Resistance 44
Froude s Calculations 20 February 2002 Resistance 45
Total Resistance Coefficient 20 February 2002 Resistance 46
Frictional Resistance Characterized by the Reynolds number, Re. From 50% of the overall resistance (high speed streamlined ships) to over 85% (slow speed tankers). Flow is laminar for low Re and turbulent for high Re (more typical in full scale ships). 20 February 2002 Resistance 47
Skin Friction Lines 20 February 2002 Resistance 48
I.T.T.C. Friction Line 20 February 2002 Resistance 49
Correlation Allowance I.T.T.C. friction line Correlation allowance: 20 February 2002 Resistance 50
Wavemaking Resistance Froude s pattern was explained by Lord Kelvin using the method of stationary phase. 20 February 2002 Resistance 51
Typical Ship Wave Pattern Calculation of wave pattern allows calculation of wave making resistance. 20 February 2002 Resistance 52
Typical Plots Typical wavemaking resistance coefficient plots exhibit multiple peaks and valleys. This has led to many optimization studies. 20 February 2002 Resistance 53
Other Components of Resistance Wind resistance. Added resistance due to waves. Added resistance due to turning. Appendage resistance. Effects of trim. Shallow water effects. Subsurface waves. 20 February 2002 Resistance 54
Operational Factors Displacement and Still-water Trim Resistance sensitive to changes in displacement and trim Sinkage and Squat Caused by bow and stern wave systems Ship sinks down without trimming at low to moderate speed Stern begins to squat as speed increases Shallow Water Generally increased resistance in shallow water Sea Conditions The heavier the seas, the higher the resistance High Winds Increase ship resistance, especially if rudder is used to maintain course Fouling Can significantly increase resistance if not controlled 20 February 2002 Resistance 55
Shallow Water Effects As the wave pattern changes, the wavemaking resistance also changes. 20 February 2002 Resistance 56
Shallow Water Effects (cont.) Water depth: h 20 February 2002 Resistance 57
Speed Reduction in Shallow Water Contours show percent speed loss. A x = max cross sectional area of the hull. h = water depth 20 February 2002 Resistance 58
Speed in Restricted Channels For a rectangular channel of width b and depth h: If a ship with cross sectional area A x and wetted girth p is in the channel: 20 February 2002 Resistance 59
Resistance Prediction If model tests are not available: ITTC for frictional resistance. Resistance standard series for wavemaking and form drag (residuary resistance). Pick the right standard series: Taylor series Holtrop Many, many others. 20 February 2002 Resistance 60
Standard Series Start with a parent hull. Build several models by systematically varying key hull geometric parameters. Test, measure, and curve fit. Parent hull form for Taylor standard series. 20 February 2002 Resistance 61
Taylor Series Typical Contours 20 February 2002 Resistance 62
Holtrop s Method See the UM notes and software implementation on the class web notes. AUTOHYDRO module of AUTOSHIP implements a number of standard series. 20 February 2002 Resistance 63
Definition of Standard Speeds Maximum Trial speed measured in calm water with maximum power output from the engines, with a clean and freshly painted hull Max speed declines with engine degradation, hull fouling, and sea state Max power output from engines cannot be sustained for long periods without suffering engine damage (redlining) Sustained Speed with engines at 80% power and clean hull in calm water Requirements usually state sustained vs. maximum speed Can be maintained for long periods as necessary Cruise Speed at which ship is expected to meet range requirement Most Economical Speed and engine combination where fuel usage is least 20 February 2002 Resistance 64
Effect of Length on Powering Hull Speed (Why does a longer ship need less power to make speed?) Speed at which the ship overtakes its bow wave and climbs the hill If v ship is the ship velocity in fps, c wave is the celerity of the transverse wave train in fps, and L w is the length of the transverse wave in feet, then: v ship glw = c = = 226. wave 2π L w By equating the wave length to the ship length (L S ), and converting fps to knots, we have the equation for hull speed (V S ): 226. V = L = 134. L S w S 1688. Since they have higher hull speeds, longer ships have lower wave resistance at the required speed, and thus need less power than their shorter counterparts 20 February 2002 Resistance 65
Additional Reading 1.4.1 Ship Resistance and Propulsion Notes 1.4.2 Reliable Performance Prediction (D. M. MacPherson) 1.4.3 Practical Hydrodynamic Optimization of a Monohull (D. Hendrix et al) 20 February 2002 Resistance 66