Resistance and propulsion
3.1 Resistance and propulsion concepts 3.1.1 Interaction between ship and propeller
Any propulsion system interacts with the ship hull. The flow field is changed by the (usually upstream located) hull. The propulsion system changes, in turn, the flow field at the ship hull. However, traditionally naval architects have considered propeller and ship separately and introduced special efficiencies and factors to account for the effects of interaction. While this decomposition is seen by many as an important aid in structuring the complex problems of ship hydrodynamics, it also hinders a system approach in design and can confuse as much as it can help. Since it is still the backbone of our experimental procedures and ingrained in generations of naval architects, the most important concepts and quantities are covered here. The hope is, however, that CFD will in future allow a more comprehensive optimization of the ship interacting with the propeller as a whole system.
The general definition 'power = force • speed' yields the effective power
RT is the total calm-water resistance of the ship excluding resistance of appendages related to the propulsive organs. Sometimes the rudder is also excluded and treated as part of the propulsion system. (This gives a glimpse of the conceptual confusion likely to follow from different conventions concerning the decomposition. Remember that in the end the installed power is to be minimized. Then 'accounting' conventions for individual factors do not matter. What is lost in one factor will be gained in another.) Vs is the ship speed. PE is the power we would have to use to tow the ship without propulsive system.
Following the same general definition of power, we can also define a power formed by the propeller thrust and the speed of advance of the propeller, the so-called thrust power:
The thrust T measured in a propulsion test is higher than the resistance Rt measured in a resistance test (without propeller). So the propeller induces an additional resistance:
1. The propeller increases the flow velocities in the aftbody of the ship which increases frictional resistance.
2. The propeller decreases the pressure in the aftbody, thus increasing the inviscid resistance.
The second mechanism dominates for usual propeller arrangements. The thrust deduction fraction r couples thrust and resistance:
t is usually assumed to be the same for model and ship, although the friction component introduces a certain scale effect. Empirical formulae for t can be found in Schneekluth and Bertram (1998), but are all plagued by large margins of uncertainty.
The propeller inflow, i.e. the speed of advance of the propeller VA, is generally slower than the ship speed due to the ship's wake. The wake is usually decomposed into three components:
• Friction wake
Due to viscosity, the flow velocity relative to the ship hull is slowed down in the boundary layer, leading in regions of high curvature (especially in the aftbody) to flow separation.
• Potential wake
In an ideal fluid without viscosity and free surface, the flow velocity at the stern resembles the flow velocity at the bow, featuring lower velocities with a stagnation point.
The steady wave system of the ship changes locally the flow as a result of the orbital velocity under the waves. A wave crest above the propeller increases the wake fraction, a wave trough decreases it.
For usual single-screw ships, the frictional wake dominates. Wave wake is only significant for Fn > 0.3. The measured wake fraction in model tests is larger than in full scale as boundary layer and flow separation are relatively larger in model scale. Traditionally, correction formulae try to consider this overpredic-tion, but the influence of separation can only be estimated and this introduces a significant error margin. So far CFD also largely failed to reproduce the wake even in model scale probably due to insufficient turbulence modelling. The errors in predicting the required power remain nevertheless small, as the energy loss due to the wake is partially recovered by the propeller. However, the errors in predicting the wake propagate completely when computing optimum propeller rpm and pitch.
The wake behind the ship without propeller is called the nominal wake. The propeller action accelerates the flow field by typically 5-20%. The wake behind the ship with operating propeller is called the effective wake. The wake distribution is either measured by laser-Doppler velocimetry or computed by CFD. While CFD is not yet capable of reproducing the wake with sufficient accuracy, the integral of the wake over the propeller plane, the wake fraction w, is predicted well. The wake fraction is defined as:
Schneekluth and Bertram (1998) give several empirical formulae to estimate w in simple design approaches. All these formulae consider only a few main parameters, but actually the shape of the ship influences the wake considerably. Other important parameter like propeller diameter and propeller clearance are also not explicitly represented in these simple design formulae.
The ratio of the effective power to the thrust power is called the hull efficiency:
The hull efficiency can thus be expressed solely by thrust deduction factor t and wake fraction w. iH can be less or greater than 1. It is thus not really an efficiency which by definition cannot be greater than 100%.
The power delivered at the propeller can be expressed by the torque and the rpm:
This power is less than the 'brake power' directly at the ship engine PB due to losses in shaft and bearings. These losses are comprehensively expressed in the shafting efficiency qS: PD = is ■ PB. The ship hydrodynamicist is not concerned with PB and can consider PD as the input power to all further considerations of optimizing the ship hydrodynamics. We use here a simplified definition for the shafting efficiency. Usually marine engineers decompose qs into a shafting efficiency that accounts for the losses in the shafting only and an additional mechanical efficiency. For the ship hydrodynamicist it suffices to know that the power losses between engine and delivered power are typically 1.5-2%.
The losses from delivered power PD to thrust power PT are expressed in the (propeller) efficiency behind ship qB: PT = qB ■ PD.
The open-water characteristics of the propeller are relatively easy to measure and compute. The open-water efficiency i 0 of the propeller is, however, different to qB. Theoretically, the relative rotative efficiency accounts for the differences between the open-water test and the inhomogeneous three-dimensional propeller inflow encountered in propulsion conditions: qB = ■ i 0. In reality, the propeller efficiency behind the ship cannot be measured and all effects not included in the hull efficiency, i.e. wake and thrust deduction fraction, are included in qR. qR again is not truly an efficiency. Typical values for single-screw ships range from 1.02 to 1.06. Schneekluth and Bertram (1998) give again simple empirical formulae for design purposes.
The various powers and efficiencies can be expressed as follows:
Pe = iH ■ Pt = iH ■ iB ■ Pd = iH ■ 10 ■ iR ■ Pd = iH ■ 10 ■ 1r ■ is ■ Pb = iD ■ is ■ Pb
The propulsive efficiency iD collectively expresses the hydrodynamic efficiencies: iD = iH ■ i0 ■ iR. Schneekluth and Bertram (1998) again give simple design estimates for iD.
3.1.2 Decomposition of resistance
As the resistance of a full-scale ship cannot be measured directly, our knowledge about the resistance of ships comes from model tests. The measured calm-water resistance is usually decomposed into various components, although all these components usually interact and most of them cannot be measured individually. The concept of resistance decomposition helps in designing the hull form as the designer can focus on how to influence individual resistance components. Larsson and Baba (1996) give a comprehensive overview of modern methods of resistance decomposition (Fig. 3.1).
- Figure 3.1 Resistance decomposition
The total calm-water resistance of a new ship hull can be decomposed into:
• Friction resistance
Due to viscosity, directly at the ship hull water particles 'cling' to the surface and move with ship speed. A short distance away from the ship, the water particles already have the velocity of an outer, quasi-inviscid flow. The region between the ship surface and the outer flow forms the boundary layer. In the aftbody of a container ship with Rn ^ 109, the boundary layer thickness may be 1 m. The rapid velocity changes in normal direction in the boundary layer induce high shear stresses. The integral of the shear stresses over the wetted surface yield the friction resistance.
• Viscous pressure resistance
A deeply submerged model of a ship will have no wave resistance, but its resistance will be higher than just the frictional resistance. The form of the ship induces a local flow field with velocities that are sometimes higher and sometimes lower than the average velocity. The average of the resulting shear stresses is then higher. Also, energy losses in the boundary layer, vortices and flow separation prevent an increase to stagnation pressure in the aftbody as predicted in an ideal fluid theory. Full ship forms have a higher viscous pressure resistance than slender ship forms.
66 Practical Ship Hydrodynamics • Wave resistance
The ship creates a typical wave system which contributes to the total resistance. In the literature, the wave system is often (rather artificially) decomposed into a primary and a secondary wave system:
- Figure 3.2 'Primary' wave system
In an ideal fluid with no viscosity, a deeply submerged body would have zero resistance (D'Alembert's paradoxon). The flow would be slower at both ends of the body and faster in the middle. Correspondingly at each end the pressure will be higher than average, reaching at one point stagnation pressure, and the pressure in the middle will be lower than average. Now imagine a body consisting of the ship hull below the calm-water surface and its mirror image at the calm-water surface (Fig. 3.3). This double body would create a certain pressure distribution at the symmetry plane (calm-water surface) in an infinite ideal fluid. Following Bernoulli's equation, we could express a corresponding surface elevation (wave height) distribution for this pressure distribution, yielding wave crests at the ship ends and a long wave trough along the middle. This is called the primary wave system. The shape of the primary wave system is speed independent, e.g. the locations of maxima, minima, and zero crossings are not affected by the speed. The vertical scale (wave height) depends quadratically on the speed.
2. Secondary wave system (Fig. 3.4)
At the free surface, a typical wave pattern is produced and radiated downstream. Even if we assume an ideal fluid with no viscosity, this wave pattern will result in a resistance. The wave pattern consists of transverse and divergent waves. In deep water, the wave pattern is limited to a wedge-shaped region with a half-angle of 19.5°. This angle is independent of the actual shape of the ship. On shallow water, the half-angle widens to 90° (for depth Froude number Fnh = 1.0) and then becomes more and more narrow for supercritical speeds above Fnh = 1. The ship
- Figure 3.4 'Secondary' wave system
produces various wave patterns which interfere with each other. The main wave patterns are created where strong changes in the geometry near the water surface occur, i.e. at the bulbous bow, the bow, the forward shoulder, the aft shoulder, and the stern. The wave length X depends quadratically on the ship speed. Unfavourable Froude numbers with mutual reinforcement between major wave systems, e.g. bow and stern waves, should be avoided. This makes, e.g., Fn = 0.4 an unfavourable Froude number. The interference effects result in a wave resistance curve with humps and hollows. If the wave resistance coefficient is considered, i.e. the wave resistance made non-dimensional by an expression involving the square of the speed, the humps and hollows become very pronounced.
In reality, the problem is more complex:
- The steepness of waves is limited. The pressure in the 'primary wave system' changes rapidly at the ship ends enforcing unrealistically steep waves. In reality, waves break here and change the subsequent 'secondary wave pattern'. At Froude numbers around 0.25 usually considerable wavebreaking starts, making this Froude number in reality often unfavourable although many textbooks recommend it as favourable based on the above interference argument for the 'secondary wave pattern'.
- The free surface results also in a dynamic trim and sinkage. This also changes the wave pattern. Even if the double-body flow around the dynamically trimmed and sunk ship is computed, this is not really the ship acting on the fluid, as the actually wetted surface (wave profile) changes the hull. The double-body flow model breaks down completely, if a transom stern is submerged, but dry at the ship speed. This is the case for many modern ship hulls. The wave resistance cannot be properly estimated by simple design formulae. It is usually determined in model tests. Although efforts to compute the wave resistance by theoretical methods date back more than 100 years, the problem is still not completely solved satisfactorily. The beginning of computational methods is usually seen with the work of the Australian mathematician Michell who in 1898 proposed an integral expression to compute the wave resistance. Today, boundary element methods have become a standard tool to compute the 'wave resistance problem', but the accurate prediction of the wave resistance came only close to a satisfactory solution by the end of the 1990s. Even then, problems remained with breaking waves and the fundamental dilemma that in reality ship resistance exists only as a whole quantity. Its separation into components is merely a hypothesis to facilitate analysis, but the theoretically cleanly divided resistance components interact and require a comprehensive approach for a completely satisfactory treatment.
Computational methods for the analysis of the wave resistance will be discussed in detail in section 3.5.1.
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