FRICTION IN SHIP RESISTANCE - A DIFFERENT APPROACH

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1 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 FRICTION IN SHIP RESISTANCE - A DIFFERENT APPROACH EBERHARD WOLFF Departamento de Metal Mecanica Instituto Tecnologico de La Paz Blvd. Forjadores 470, 3080 La Paz, Baja California Sur MEXICO seewolff605@yahoo.com.mx Abstract: - Friction is considered to form 50% and more of the resistance force on a vessel moving in water. Computing of the total resistance force usually is realized with special computer programs - which depend on the results of drawing tests with scaled models - based on the wave patterns resulting from potential flow considerations. Considering inertia force of the displaced water by the bow of the vessel as the main part of the total resistance force, this force can be calculated as the impulse force of a water jet hitting the bow zone. nowledge of friction force on all the wetted area could complete a computation of the total resistance force without the need of model towing tests. Measurements of the friction force created by a water jet hitting a flat plate, show a clear tendency of decreasing friction with increasing jet velocity and impact angle. ey-words: - fluid friction, ship resistance, inertia force, water jet, equilibrium, pendulum Introduction Friction between water and a ship hull is considered to be more than 50% of the total resistance force [], [4], [5], [6], while in a Pelton water turbine, which shows similar conditions as a moving ship, friction must be less than 5%, due to the high efficiency of these turbines which is around 90% if the turbine works at design conditions. Among other differences between a ship and a turbine, there is a difference in the relative velocity between water and the solid surface. But both have in common the condition of a water movement below a static pressure close or equal to the atmospheric pressure, but the relative velocity of the water stream to the solid surface is for a ship hull around 5 m/s, and for a Pelton turbine around 50 m/s - about 0 times more. Problem Formulation Friction has never been calculated or measured directly as part of the resistance force on a ship hull. The computation of the total resistance force of a ship moved in the water is up to now done by extensive computer programs [4], [5], [6], plus drawing tests with models which provide indispensable information for the computing process, which is based principally on the wave pattern generated by the model, using potential flow theory. Friction is the remaining part to the measured total force with the model, as it supposedly doesn't contribute any part to the wave generation. So, neither the total resistance force, nor the friction force can be calculated directly, and it is not even known, which parameters have an important influence on friction magnitude. 3 Problem Solution 3. Calculation of the Inertia Resistance Force When the ship moves forward, its bow divides a water mass in two equal parts, which are accelerated sidewards until the maximum width ISSN: Page ISBN:

2 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 of the hull. This movement can also be described as a water jet of the same section as the hull at its maximum width, which hits the bow and is accelerated to both sides. To simplify the following calculations, the bow is considered as a prismatic wedge [8]. For such a prismatic body (Fig.), being partially submerged, is the resulting force which can be expressed with a vector equation: 0 = + I + I + I 0, With α = 0º, will be 0 (flat plate condition); and for α/ = 90º, will be a maximum (jet hits the plate perpendicularly). The calculation of the resistance force as the inertia force of the sideways accelerated water mass is explained for a prismatic shaped body in Fig.3 v A I 0 I α 76º B 7,5º I Fig. Forces on a prismatic shaped body in a steady flow C and calculated according to the force polygon in Fig. as: = ρ b h v [ cos(α/)] () with ρ = water density, b = maximum bow width, h = distance of waterline to submerged bottom, v = relative velocity between water and hull. Fig. Force Polygon I I I 0 α/ Fig.3 Fluid displacement with different angles at a constant flow velocity For different angles of a prismatic bow which moves with a constant velocity as shown in Fig.3, the water will take about twice the time to go from "A" to "C" as from "B" to C. This means that the longer this time is, the smaller is the acceleration or inertia force, and the smaller will be the total resistance force. This relationship between the bow angle and the total resistance force has been measured in 006 [8]. The two prismatic bodies schematically drawn in Fig. 3, only differed in the bow angle. ISSN: Page ISBN:

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 The total resistance force was for the body with 7,5º bow angle up to 44% less than for the 76º

3 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 The total resistance force was for the body with 7,5º bow angle up to 44% less than for the 76º angle, in spite of its larger wetted area, which was in this case 73% larger than the area of the 7,5º body. The relative velocity was approximately,5 m/s. Although there was a wide gap between measured and calculated values of resistance force, and friction had not been considered so far in these calculations, it seemed improbable that friction could be 50% or more of the total resistance force. 3. Measuring Friction To measure the friction force of water on a solid body, a pendulum device was built, consisting of a flat plate which was hanging on 4 thin copper wires of exactly the same length from a horizontal plate. The holes for the wires were located at the same distances one from another in both plates, so the pendulum plate stayed horizontally while deviated by the water jet (Fig.4). Adjustable parameters have been the nozzle diameter (3 nozzles of 6,35 mm diameter, 9,5 mm diameter and,7 mm diameter), the jet velocity (varying the volume flow) and the impact angle. As the pendulum plate also moves upwards as being deviated sidewards by the water jet, there exists always an equilibrium between the horizontal component W h of its gravity force W with the friction force of the water jet on the plate (fig.5 and 6), if the jet velocity stays constant. The test conditions meet approximately the conditions of the inertia force calculations described in the former chapter, except the velocity of the jet (in the jet hitting the flat plate, the velocity of the deviated jet should diminish due to friction, in the flow around the bow it should increase due to the acceleration force). γ W h x W γ Fig.5 Horizontal component of weight force Fig.4 Measuring device for friction Taking in account the existence of a friction force, the force polygon can be modified as shown in Fig.6. ISSN: Page 3 ISBN:

4 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 I 0 * Measuring the deviation angle γ of the right back wire to a cero line (fig. 5), the friction force on the plate can be calculated as a percentage of the total reaction force according to the following equation: 4 F Q ρ senα = + () π d W tanγ α I β F Fig.6 Modified force polygon with friction force The reaction force will have an angle β to the plate which is less than 90 degrees, due to friction. Friction force is the horizontal component of the reaction force. * is the reaction force without friction. X is the horizontal displacement of the plate (Fig.5), measured as the horizontal distance of the right back-side wire at its fix point on the plate, to the reference line painted on the background ( Fig.4). All the tests have been documented on digital photos, which have been taken from a fixed distance and height, perpendicularly to the plate. Impact angle α and deviation angle γ have been measured on the computer screen at a constant amplification. As γ turned out to be relatively small, a direct measuring of the angle was replaced by measuring the distance "x", which is much more precise. As shown in the photo Fig.4, the clear line which marks the impact angle is not identical with the centre line of the nozzle. This is because of the curvature of the water jet at low velocities (due to gravity force), which is considerable at a certain distance between nozzle and plate. I I * I * where Q is the volume flow, W the weight force of the plate and d the diameter of the nozzle. Formula () considers that the entire impacting jet is deviated forewards, but actually, part of the jet is deviated backwards. There is also a deviation sidewards, as we have a tridimensional case, but most of the water deviated to the sides contributes with components in the directions covered by the two dimensional considerations, and is anyway only significant at bigger impact angles close to 90 degrees, which are not considered in this work, as there are no ships which have a bow angle close to 80º. The part of the jet which is deviated backwards depends on the impact angle α. The bigger the angle, the more is reflected backwards. It is convenient to express this relationship as a quotient: I I I is the jet backwards. cosα = + cosα (3) For α = 0º, I /I will be 0, and for α = 90º, I /I will be. As the measured friction force includes the force of the jet reflected backwards, a correction has to be made in the formula (), and the correction factor has to be added to the calculated value of F /: ISSN: Page 4 ISBN:

5 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 F corr. = F I + I (4) The results of the tests have been plotted after the corrections in Fig.7, with the friction factor F / as a function of the impact angle α, and the jet velocity v as a second variable. The shaded area is marking the limits for normal bow angles. These results show that the friction is depending on the impact velocity of the jet. The diminution of friction in the covered range of impact velocity, with increasing velocity, is considerable. The curves converge for cero impact angle in 00% of friction of the total force, which can be easily confirmed as the jet only will touch the plate without causing any force on it. Another converging point is a 90º impact angle, where friction seems to be cero. This is because of the jet being deflected in equal portions to all Sides, and the opposite friction force portions compensate each other. However, the relationship of friction in the shaded area (which is the zone where all bow angles are located) to the impact angle is obvious and there may be found a reasonable explication. 4 Conclusions The main aim of this work has been to find a relationship between friction force and parameters which are influencing in the movement of a ship in the water. As the total resistance force, of which friction forms part, is presently not being calculated directly, but based on wave patterns and model drawing tests, a possible way of calculating this force is presented, based on inertia forces of the displaced water mass. As these movements can be interpreted as a water stream hitting the bow of the ship, this concept was transferred to the measuring concept of a water jet hitting a flat plate. The force created by a fluid jet on a flat plate is calculated by the equilibrium of the impulse forces and the reaction force, as well known in fluid mechanics. The results of these measurements show an acceptable precision, despite of the simplicity of the measurement array. According to Fig.7, that friction force depends at least on the impact velocity and on the impact angle. The wetted area is also important in relation to friction force, but only as a percentage of the total force and not as an absolute value. This means, that in a ship with a large bow angle, friction will be a small part of the total resistance forced, and a ship with a small bow angle will have a high percentage of friction in the total resistance force, which is well known in fast sailing vessels like catamarans. That friction force decreases with incrementing velocity, could explain finally the fact that in Pelton turbines exists such a small amount of friction. References: [] Lawrence C. Doctor, Wave Generation of High Speed ships, The Australian Naval Architect, August 003 [] P.A. rogstad, R.A. Antonia, Surface roughness effects in Turbulent Boundary Layers, Experiments in Fluids, Nº 7, 999 [3] Hong Gun Sung, Stephan T. Grilli, Numerical Modelling of Nonlinear Surface Waves Caused by Surface Effect Ships, Dynamics and inematics, Proceedings of the 5 th International Offshore and Polar Engineering Conference, Seoul, orea, June 9-4, 005 [4] Justus Heimann, CFD Based Optimization of the Wave-Making Characteristics of Ship Hulls. PhD. Thesis, Technical University Berlin, Germany, March 005 ISSN: Page 5 ISBN:

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 [5] MARIN (Maritime Research Institute Netherlands); RAPID, Calculation of Wave Resistance and

6 5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 5-7, 008 [5] MARIN (Maritime Research Institute Netherlands); RAPID, Calculation of Wave Resistance and Potential Flow., WEB publication 006 [6] Shin Hyung Rhee, Greg Stuckert, Computational Fluid Dynamics, A Powerful Marine Design Tool, Mechanical Engineering Online, ASME, 9/005 [7] Claudio Mataix, Mecanica de Fluidos y Maquinas Hidraulicas, Ed. Harla, 993 [8] Eberhard Wolff, Propuesta de Calculo Para La Fuerza de Resistencia De Cuerpos Flotantes en el Agua, Unpublished Investigation Report, Instituto Tecnologico de La Paz, Mexico, Jan ISSN: Page 6 ISBN:

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PhysicsAndMathsTutor.com 1 1. Millikan determined the charge on individual oil droplets using an arrangement as represented in the diagram. The plate voltage necessary to hold a charged droplet stationary